Bibliography


  1. Albertson, Michael. 1998. “You Can’t Paint Yourself into a Corner.” Journal of Combinatorial Theory, Series B 73: 189–94. https://doi.org/doi.org/10.1006/jctb.1998.1827.
  2. Alon, Noga. 2003. “A Simple Algorithm for Edge-Coloring Bipartite Multigraphs.” Information Processing Letters 85 (6): 301–2. https://doi.org/10.1016/S0020-0190(02)00446-5.
  3. Amahashi, Atsushi. 1985. “On Factors with All Degrees Odd.” Graphs and Combinatorics 1: 111–14. https://doi.org/10.1007/BF02582935.
  4. Appel, Kenneth, and Wolfgang Haken. 1977a. “Every Planar Map Is Four Colorable. Part I: Discharging.” Illinois Journal of Mathematics 21: 429–90. https://doi.org/10.1215/ijm/1256049011.
  5. ———. 1977b. “Every Planar Map Is Four Colorable. Part II: Reducibility.” Illinois Journal of Mathematics 21: 491–567. https://doi.org/10.1215/ijm/1256049012.
  6. Ball, W. W. Rouse. 1905. Mathematical Recreations and Essays. Fourth edition. New York, NY: Macmillan; Company. https://www.gutenberg.org/ebooks/26839.
  7. Berkeley Math Circle. 2005. “7th Bay Area Mathematical Olympiad.” https://www.bamo.org/archives/examfiles/bamo2005examsol.pdf.
  8. Bondy, John A., and Václav. Chvátal. 1976. “A Method in Graph Theory.” Discrete Mathematics 15 (2): 111–35. https://doi.org/10.1016/0012-365X(76)90078-9.
  9. Borchardt, Carl Wilhelm. 1860. “Über Eine Interpolationsformel für Eine Art Symmetrischer Functionen Und über Deren Anwendung.” Mathematische Abhandlungen Der Königlichen Akademie Der Wissenschaften Zu Berlin, 1–20. https://archive.org/details/abhandlungenderk1860deut/page/n245.
  10. Bottin, Matteo, Giovanni Boschetti, and Giulio Rosati. 2022. “Optimizing Cycle Time of Industrial Robotic Tasks with Multiple Feasible Configurations at the Working Points.” Robotics 11 (1): 16. https://doi.org/10.3390/robotics11010016.
  11. de Bruijn, Nicolaas Govert. 1946. “A Combinatorial Problem.” Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen 49: 758–64.
  12. Campos, Marcelo, Simon Griffiths, Robert Morris, and Julian Sahasrabudhe. 2023. “An Exponential Improvement for Diagonal Ramsey.” arXiv Preprint. https://arxiv.org/abs/2303.09521.
  13. Cayley, Arthur. 1857. “On the Theory of the Analytical Forms Called Trees.” Philosophical Magazine 13: 172–76. https://rcin.org.pl/Content/173708/PDF/WA35_185808_12807-3_art-45.pdf.
  14. Chaitin, Gregory, Marc Auslander, Ashok Chandra, John Cocke, Martin Hopkins, and Peter Markstein. 1981. “Register Allocation via Coloring.” Computer Languages 6: 47–57. https://doi.org/10.1016/0096-0551(81)90048-5.
  15. Chen, Guantao, and Xingxing Yu. 2002. “A Note on Fragile Graphs.” Discrete Mathematics 249: 41–43. https://doi.org/10.1016/S0012-365X(01)00226-6.
  16. Chvátal, Václav. 1973. “Tough Graphs and Hamiltonian Circuits.” Discrete Mathematics 5: 215–28. https://doi.org/10.1016/0012-365X(73)90138-6.
  17. Chvátal, Václav, and Pál Erdős. 1972. “A Note on Hamiltonian Circuits.” Discrete Mathematics 2: 111–13. https://doi.org/10.1016/0012-365X(72)90079-9.
  18. Chvátal, Václav, and Peter Hammer. 1977. “Aggregation of Inequalities in Integer Programming.” Annals of Discrete Mathematics 1: 145–62.
  19. Conway, John H. 2017. “Five $1,000 Problems (Update 2017).” 2017. https://oeis.org/A248380/a248380.pdf.
  20. Coolsaet, K., S. D’hont, and J. Goedgebeur. 2023. “House of Graphs 2.0: A Database of Interesting Graphs and More.” Discrete Applied Mathematics. 2023. https://doi.org/10.1016/j.dam.2022.10.013.
  21. Cranston, Daniel, and Landon Rabern. 2015. “Brooks’ Theorem and Beyond.” Journal of Graph Theory 80. https://doi.org/10.1002/jgt.21847.
  22. Deuerlein, Jochen W. 2008. “Decomposition Model of a General Water Supply Network Graph.” Journal of Hydraulic Engineering 134. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:6(822).
  23. Dirac, Gabriel. 1952. “Some Theorems on Abstract Graphs.” Proceedings of the London Mathematical Society 3 (1): 69–81. https://doi.org/10.1112/plms/s3-2.1.69.
  24. ———. 1966. “Short Proof of Menger’s Graph Theorem.” Mathematika 13: 42–44. https://doi.org/10.1112/S0025579300004162.
  25. Edmonds, Jack, and Richard M. Karp. 1972. “Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems.” Journal of the ACM 19: 248–64. https://doi.org/10.1145/321694.321699.
  26. Ehrenfeucht, Andrzej, Vance Faber, and Henry Kierstead. 1984. “A New Method of Proving Theorems on Chromatic Index.” Discrete Mathematics 52. https://doi.org/10.1016/0012-365X(84)90078-5.
  27. Eppstein, David. “Twenty-One Proofs of Euler’s Formula: \(V-E+F=2\).” Accessed December 21, 2025. https://ics.uci.edu/~eppstein/junkyard/euler/.
  28. Erdős, Pál. 1947. “Some Remarks on the Theory of Graphs.” Bulletin of the American Mathematical Society 53 (4): 292–94. https://doi.org/10.1090/S0002-9904-1947-08785-1.
  29. ———. 1964. “On an Extremal Problem in Graph Theory.” Colloquium Mathematicum 13: 251–54. https://doi.org/10.4064/cm-13-2-251-254.
  30. Erdős, Pál, and Tibor Gallai. 1960. “Gráfok Előírt Fokszámú Pontokkal.” Matematikai Lapok 11: 264–74. https://www.renyi.hu/~p_erdos/1961-05.pdf.
  31. Esfahanian, Abdol, and S. L. Hakimi. 1984. “On Computing the Connectivities of Graphs and Digraphs.” Networks 14: 355–66. https://doi.org/10.1002/net.3230140211.
  32. Euler, Leonhard. 1758. “Elementa Doctrinae Solidorum.” Novi Commentarii Academiae Scientiarum Petropolitanae 4: 109–40. https://scholarlycommons.pacific.edu/euler-works/230/.
  33. Federico, P. J. 1982. Descartes on Polyhedra: A Study of the “De Solidorum Elementis”. Sources in the History of Mathematics and Physical Sciences. Springer.
  34. Ford Jr., L. R., and D. R. Fulkerson. 1956. “Maximal Flow Through a Network.” Canadian Journal of Mathematics 8: 399–404. https://doi.org/10.4153/CJM-1956-045-5.
  35. Frucht, Robert. 1949. “Graphs of Degree Three with a Given Abstract Group.” Canadian Journal of Mathematics 1: 365–78. https://doi.org/10.4153/CJM-1949-033-6.
  36. Gardner, Martin. 1997. “M-Pire Maps.” In The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications, by Martin Gardner, 85–100. New York, NY: Springer New York.
  37. ———. 2008. “The Five Platonic Solids.” In Origami, Eleusis, and the Soma Cube, by Martin Gardner, 1–10. New York, NY: Cambridge University Press.
  38. Gonthier, Georges. 2008. “Formal Proof—the Four-Color Theorem.” Notices of the American Mathematical Society 55: 1382–93.
  39. Graham, Ronald, and Daniel Kleitman. 1973. “Increasing Paths in Edge Ordered Graphs.” Period. Math. Hungar. 3: 141–48. https://doi.org/10.1007/BF02018469.
  40. Greenwood, Robert, and Andrew Gleason. 1955. “Combinatorial Relations and Chromatic Graphs.” Canadian Journal of Mathematics 7: 1–7. https://doi.org/10.4153/CJM-1955-001-4.
  41. de Grey, Aubrey. 2018. “The Chromatic Number of the Plane Is at Least 5.” arXiv Preprint. https://arxiv.org/abs/1804.02385.
  42. Grötzsch, Herbert. 1959. “Zur Theorie Der Diskreten Gebilde, VII: Ein Dreifarbenansatz für Dreikreisfrei Netze Auf Der Kugel.” Wissenschaftliche Zeitschrift Der Martin-Luther-Universität Halle-Wittenberg: Mathematisch-Naturwissenschaftliche Reihe 8: 109–20.
  43. Gupta, Parth, Ndiame Ndiaye, Sergey Norin, and Louis Wei. 2024. “Optimizing the CGMS Upper Bound on Ramsey Numbers.” arXiv Preprint. https://arxiv.org/abs/2407.19026.
  44. Guy, Richard. 1988. “The Strong Law of Small Numbers.” The American Mathematical Monthly 95: 697–712. https://doi.org/10.1080/00029890.1988.11972074.
  45. Gyárfás, András, Jeno X. Lehel, and Zsolt Czap Tuza. 1988. “Clumsy Packing of Dominoes.” Discrete Mathematics 71 (1): 33–46. https://doi.org/10.1016/0012-365X(88)90028-3.
  46. Hakimi, S. L. 1962. “On Realizability of a Set of Integers as Degrees of the Vertices of a Linear Graph. I.” Journal of the Society for Industrial and Applied Mathematics 10 (3): 496–506. https://doi.org/10.1137/0110037.
  47. Hall, Philip. 1931. “On Representatives of Subsets.” Journal of the London Mathematical Society 10 (1): 26–30. https://doi.org/10.1112/jlms/s1-10.37.26.
  48. Hammack, Richard. 2018. Book of Proof. https://richardhammack.github.io/BookOfProof/.
  49. Harary, Frank. 1962. “The Maximum Connectivity of a Graph.” Proceedings of the National Academy of Sciences of the United States of America 48: 1142–46. https://doi.org/10.1073/pnas.48.7.1142.
  50. Harary, Frank, and Robert Norman. 1960. “Some Properties of Line Digraphs.” Rendiconti Del Circolo Matematico Di Palermo 9: 161–68. https://doi.org/10.1007/BF02854581.
  51. Harchol-Balter, Mor. 2013. Performance Modeling and Design of Computer Systems. Cambridge University Press. https://www.cs.cmu.edu/~harchol/PerformanceModeling/book.html.
  52. Havel, Václav. 1955. “Poznámka o Existenci Konečných Grafů.” Časopis Pro pěstování Matematiky 80 (4): 477–80. https://doi.org/10.21136/CPM.1955.108220.
  53. He, Yuan, Hao Ren, Yunhao Liu, and Baijian Yang. 2009. “On the Reliability of Large-Scale Distributed Systems — a Topological View.” Computer Networks 53: 2140–52. https://doi.org/10.1016/j.comnet.2009.03.012.
  54. Heawood, Percy J. 1890. “Map Colour Problem.” Quarterly Journal of Pure and Applied Mathematics 24: 332–38.
  55. Hedayat, Samad, and Walter T. Federer. 1975. “On the Nonexistence of Knut Vik Designs for All Even Orders.” The Annals of Statistics 3 (2): 445–47. https://doi.org/10.1214/aos/1176343068.
  56. Hoffman, Alan, and Robert Singleton. 1960. “On Moore Graphs with Diameters 2 and 3.” IBM Journal of Research and Development 4: 497–504. https://doi.org/10.1147/rd.45.0497.
  57. Holton, Derek, and John Sheehan. 1993. The Petersen Graph. Australian Mathematical Society Lecture Series. Cambridge University Press.
  58. Hudson, Hud. 2003. “Four Colors Do Not Suffice.” The American Mathematical Monthly 110: 417–23. https://doi.org/10.1080/00029890.2003.11919979.
  59. Jackson, Brad, and Gerhard Ringel. 1984. “Solution of Heawood’s Empire Problem in the Plane.” Journal für Die Reine Und Angewandte Mathematik 347: 146–53. https://doi.org/10.1515/crll.1984.347.146.
  60. Kainen, Paul C. 1974. “A Generalization of the 5-Color Theorem.” Proceedings of the American Mathematical Society 45: 450–53. https://doi.org/10.2307/2039977.
  61. Kleber, Michael, and Ravi Vakil. 2002. “The Best Card Trick.” The Mathematical Intelligencer 24: 9–11. https://doi.org/10.1007/BF03025305.
  62. Kőnig, Dénes. 1916. “Über Graphen Und Ihre Anwendung Auf Determinantentheorie Und Mengenlehre.” Mathematische Annalen 77: 453–65. https://doi.org/10.1007/BF01456961.
  63. ———. 1931. “Gráfok és mátrixok.” Matematikai és Fizikai Lapok 38: 116–19.
  64. ———. 2001. Theorie Der Endlichen Und Unendlichen Graphen. Vol. 72. American Mathematical Society.
  65. Kruskal, Joseph B. 1956. “On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem.” Proceedings of the American Mathematical Society 7 (1): 48–50. https://doi.org/10.2307/2033241.
  66. Kullman, David. 1979. “The Utilities Problem.” Mathematics Magazine 52: 299–302. https://doi.org/10.1080/0025570X.1979.11976807.
  67. Kuratowski, Casimir. 1930. “Sur Le Problème Des Courbes Gauches En Topologie.” Fundamenta Mathematicae 15: 271–83. https://doi.org/10.4064/fm-15-1-271-283.
  68. Lee, William Wallace. 1950. Math Miracles. Durham, N.C.: Seeman Printery.
  69. Li, Ben P. C., and Michel Toulouse. 2010. “Maximum Leaf Spanning Tree Problem for Grid Graphs.” Journal of Combinatorial Mathematics and Combinatorial Computing 73: 181. https://combinatorialpress.com/jcmcc-articles/volume-073/maximum-leaf-spanning-tree-problem-for-grid-graphs/.
  70. Lovász, László, and Michael D. Plummer. 1986. Matching Theory. North Holland.
  71. Lovelace, David C. 2003. “RPS-7.” 2003. https://umop.com/rps7.htm.
  72. Menger, Karl. 1927. “Zur Allgemeinen Kurventheorie.” Fundamenta Mathematicae 10: 96–115. https://doi.org/10.4064/fm-10-1-96-115.
  73. Miller, Mirka, and Jozef Širáň. 2013. “Moore Graphs and Beyond: A Survey of the Degree/Diameter Problem.” Electronic Journal of Combinatorics. https://doi.org/10.37236/35.
  74. Moore, Edward F. 1959. “The Shortest Path Through a Maze.” In Proc. Internat. Sympos. Switching Theory 1957, Parts I,II, 285–92. The Annals of the Computation Laboratory of Harvard University, Vols. XXIX, XXX. Harvard Univ. Press, Cambridge, MA.
  75. Moser, Leo, and William Moser. 1961. “Problems for Solution (P10).” Canadian Mathematical Bulletin 4: 187–89. https://doi.org/10.1017/S0008439500025753.
  76. Mycielski, Jan. 1955. “Sur Le Coloriage Des Graphs.” Colloquium Mathematicum 3: 161–62. https://doi.org/10.4064/cm-3-2-161-162.
  77. Newstead, Clive. 2024. An Infinite Descent into Pure Mathematics. https://infinitedescent.xyz/.
  78. OEIS Foundation Inc. 2026. “Entry A000055 in the On-Line Encyclopedia of Integer Sequences.” https://oeis.org/A000055.
  79. ———. 2026. “Entry A000109 in the On-Line Encyclopedia of Integer Sequences.” https://oeis.org/A000109.
  80. ———. 2026. “Entry A002851 in the On-Line Encyclopedia of Integer Sequences.” https://oeis.org/A002851.
  81. ———. 2026. “Entry A380996 in the On-Line Encyclopedia of Integer Sequences.” https://oeis.org/A380996.
  82. Pólya, George. 1921. “Uber Die ‘Doppelt-Periodischen’ lösungen Des \(n\)-Damen-Problems.” W. Ahrens, Mathematische Unterhaltungen Und Spiele 1: 364–74.
  83. ———. 1937. “Kombinatorische Anzalbestimmungen für Gruppen, Graphen, Und Chemische Verbindungen.” Acta Mathematica 68 (1): 145–254. https://doi.org/10.1007/BF02546665.
  84. ———. 1945. How to Solve It. Princeton University Press.
  85. Pratt, Rob. 2023. “16 Queens Puzzle.” 2023. https://puzzling.stackexchange.com/a/122418/47819.
  86. Princeton University Math Club. 2019. “2019 Princeton University Mathematics Competition.” https://pumac.princeton.edu/archives/#2019.
  87. Prüfer, Heinz. 1918. “Neuer Beweis Eines Satzes über Permutationen.” Arch. Math. Phys 27: 742–44.
  88. Radziszowski, Stanisław. 2024. “Small Ramsey Numbers.” Electronic Journal of Combinatorics. https://doi.org/10.37236/21.
  89. Ramsey, Frank. 1930. “On a Problem of Formal Logic.” Proceedings of the London Mathematical Society 2: 264–86. https://doi.org/10.1112/plms/s2-30.1.264.
  90. Robertson, Neil, Daniel Sanders, Paul Seymour, and Robin Thomas. 1997. “The Four-Colour Theorem.” Journal of Combinatorial Theory, Series B 70: 2–44. https://doi.org/10.1006/jctb.1997.1750.
  91. Shannon, Claude. 1949. “A Theorem on Coloring the Lines of a Network.” Journal of Mathematics and Physics 28: 148–52. https://doi.org/10.1002/sapm1949281148.
  92. SimpleMaps.com. 2010–2025. “Free GIS Maps of Switzerland.” https://simplemaps.com/gis/country/ch.
  93. Sperner, Emanuel. 1928. “Ein Satz über Untermengen Einer Endlichen Menge.” Mathematische Zeitschrift 27 (1): 544–48. https://doi.org/10.1007/BF01171114.
  94. Steinitz, Ernst. 1894. Über Die Konstruction Der Configurationen \(n_3\). Druck v. Dr. R. Galle.
  95. Sumner, David. 1974. “Graphs with 1-Factors.” Proceedings of the American Mathematical Society 42: 8–12. https://doi.org/10.2307/2039666.
  96. Thomasson, Dan. 2002. “Knight’s Tour Golden Star.” 2002. http://danthomasson.com/kt-golden-star.html.
  97. Trudeau, Richard J. 1993. Introduction to Graph Theory. Dover Publications, Inc.
  98. Tutte, William Thomas. 1946. “On Hamiltonian Circuits.” Journal of the London Mathematical Society 21: 98–101. https://doi.org/10.1112/jlms/s1-21.2.98.
  99. ———. 1947. “The Factorization of Linear Graphs.” Journal of the London Mathematical Society 1 (2): 107–11. https://doi.org/10.1112/jlms/s1-22.2.107.
  100. ———. 1959. “Matroids and Graphs.” Transactions of the American Mathematical Society 90: 527–52. https://doi.org/10.2307/1993185.
  101. Veblen, Oswald. 1912. “An Application of Modular Equations in Analysis Situs.” Annals of Mathematics, Second Series 14 (1): 86–94. https://doi.org/10.2307/1967604.
  102. Vizing, Vadim. 1964. “On an Estimate of the Chromatic Class of a \(p\)-Graph.” Diskretnyi Analiz 3: 25–30.
  103. Wagner, Klaus. 1937. “Über Eine Eigenschaft Der Ebenen Komplexe.” Mathematische Annalen 114: 570–90. https://doi.org/10.1007/BF01594196.
  104. West, Douglas B. 1996. Introduction to Graph Theory. Prentice Hall.
  105. Whitney, Hassler. 1932a. “Congruent Graphs and the Connectivity of Graphs.” American Journal of Mathematics 54: 150–68. https://doi.org/10.2307/2371086.
  106. ———. 1932b. “Non-Separable and Planar Graphs.” Transactions of the American Mathematical Society 34: 339–62. https://doi.org/10.1090/S0002-9947-1932-1501641-2.
  107. Wilson, Robin J. 2002. Four Colors Suffice: How the Map Problem Was Solved. Princeton, NJ: Princeton University Press.
  108. Winkler, Peter. 2008. “Puzzled: Solutions and Sources.” Communications of the ACM 51 (9): 103–3. https://doi.org/10.1145/1378727.1389570.


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