Density of Monochromatic Infinite Subgraphs
Tóm tắt
Từ khóa
Tài liệu tham khảo
P. Allen, B. Roberts and J. Skokan: Ramsey numbers of squares of paths, Electronic Notes in Discrete Mathematics 49 (2015), 637–641.
F. Benevides, T. Luczak, J. Skokan, A. Scott and M. White: Monochromatic cycles in 2-coloured graphs, Combinatorics, Probability, and Computing, 21 (2012), 57–87.
C. Berge: Graphs and Hypergraphs, second revised edition, Amsterdam: North-Holland Publishing Co., 1976.
C. Chvatál, V. Rödl, E. Szemerédi and W. T. Trotter: The Ramsey number of a graph with bounded maximum degree, Journal of Combinatorial Theory, Series B 34 (1983), 239–243.
J. Corsten: Personal communication.
M. Elekes, D. Soukup, L. Soukup and Z. Szentmiklóssy: Decompositions of edge-colored infinite complete graphs into monochromatic paths, Discrete Mathematics 340 (2017), 2053–2069.
P. Erdős, A. Gyárfás and L. Pyber: Vertex coverings by monochromatic cycles and trees, Journal of Combinatorial Theory, Series B 51 (1991), 90–95.
L. Gerencsér and A. Gyárfás: On Ramsey-type problems, Ann. Sci. Budapest. Ëotvös Sect. Math 10 (1967), 167–170.
H. Guggiari: Monochromatic paths in the complete symmetric infinite digraph, manuscript, arXiv:1710.10900, (2017).
A. Gyárfás: Partition covers and blocking sets in hypergraphs, MTA SZTAKI Tanulmányok 71, 1977.
A. Gyárfás and J. Lehel: A Ramsey-type problem in directed and bipartite graphs, Periodica Mathematica Hungarica 3 (1973), 299–304.
A. Gyárfás, M. Ruszinkó, G. Sárközy and E. Szemerédi: Three-color Ramsey numbers for paths, Combinatorica 27 (2007), 35–69.
A. xGyárfás and G. Sárközy: Star Versus Two Stripes Ramsey Numbers and a Conjecture of Schelp, Combinatorics, Probability and Computing 21 (2012), 179–186.
A. Gyárfás, G. Sárközy and E. Szemerédi: The Ramsey number of diamond-matchings and loose cycles in hypergraphs, Electron. J. Combin 15 (2008), #R126.
P. Haxell, T. Luczak, Y. Peng, V. Rödl, A. Ruciński and J. Skokan: The Ramsey number for 3-uniform tight hypergraph cycles, Combinatorics, Probability and Computing 18 (2009), 165–203.
P. Haxell, T. Luczak, Y. Peng, V. Rödl, A. Ruciński, M. Simonovits and J. Skokan: The Ramsey number for hypergraph cycles I, Journal of Combinatorial Theory, Series A 113 (2006), 67–83.
M. Hrušàk: Combinatorics of filters and ideals, Set theory and its applications 533, Contemp. Math., Amer. Math. Soc, Providence, RI (2011), 29–69.
P. Komjáth and V. Totik: Problems and theorems in classical set theory, Springer Science & Business Media (2006).
J. Komlós and M. Simonovits: Szemerédi’s regularity lemma and its applications in graph theory, Bolyai Society Mathematical Studies 2, Combinatorics, Paul Erdős is Eighty (Vol. 2), Budapest (1996), 295–352.
M. Las Vergnas: Sur l’existence des cycles hamiltoniens dans un graphe, CR Acad, Sci. Paris, Sér. A 270 (1970), 1361–1364.
S. Letzter: Path Ramsey number for random graphs, Combinatorics, Probability and Computing 25 (2016), 612–622.
A. Pokrovskiy: Partitioning edge-coloured complete graphs into monochromatic cycles and paths, Journal of Combinatorial Theory, Series B 106 (2014), 70–97.
H. Raynaud: Sur le circuit hamiltonien bi-coloré dans les graphes orientés, Periodica Mathematica Hungarica 3 (1973), 289–297.
E. Szemerédi: Regular Partitions of Graphs, Colloques Internationaux C.N.R.S -Problèmes Combinatoires et Théorie des Graphes 260 (1976), 399–401.
Z. Tuza: Ryser’s conjecture on transversals of r-partite hypergraphs, Ars Combinatoria 16 (1983), 201–209.