Fraternal augmentations, arrangeability and linear Ramsey numbers

European Journal of Combinatorics

Volumn 30, Issue 7, 2009, Pages 1696-1703

  Nešetřil, Jaroslav ^a,b   Ossona de Mendez, Patrice ^c  

^a CHARLES UNIVERSITY   (Czech Republic)

^b Institute of Theoretical Computer Science (ITI)   (Czech Republic)

^c CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67650429725     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejc.2009.03.012     Document Type: Article

References (26)

1. Alon N. Subdivided graphs have linear Ramsey numbers. J. Graph Theory 18 4 (1994) 343-347
2. Beck J. Combinatorial Games: Tic - Tac - Toe Theory (2008), Cambridge Univ. Press
3. Burr S.A., and Erdo{double acute}s P. On the Magnitude of Generalized Ramsey Numbers for Graphs. Colloquia Mathematica Societatis Janos Bolyai 10 Infinite and Finite Sets vol. 1 (1975) 214-240
4. Chen G., and Schelp R.H. Graphs with linearly bounded Ramsey numbers. J. Combin. Theory Ser. B 57 1 (1993) 138-149
5. Chvátal V., Rödl V., Szemerédi E., and Trotter Jr. W.T. The Ramsey number of a graph with bounded maximum degree. J. Combin. Theory Ser. B 34 3 (1983) 239-243
6. Eaton N. Ramsey numbers for sparse graphs. Discrete Math. 185 (1998) 63-75
7. Gavril F., and Urrutia J. An algorithm for fraternal orientation of graphs. Inform. Process. Lett. 41 (1992) 271-274
8. Graham R.L., Rödl V., and Ruciński A. On graphs with linear Ramsey numbers. J. Graph Theory 35 (2000) 176-192
9. Graham R.L., Rödl V., and Ruciński A. On bipartite graphs with linear Ramsey numbers Paul Erdös and his mathematics. Combinatorica 21 (2001) 199-209
10. Graham R.L., Spencer J., and Rothschild B.L. Ramsey Theory (1980), Wiley, New York
11. Kierstead H.A., and Trotter W.T. Planar graph coloring with an uncooperative partner. J. Graph Theory 18 6 (1994) 569-584
12. Kostochka A.V., and Rödl V. On graphs with small Ramsey numbers. J. Graph Theory 37 (2001) 198-204
13. Kostochka A.V., and Rödl V. On graphs with small Ramsey numbers II. Combinatorica 24 3 (2004) 389-401
14. Kostochka A.V., and Sudakov B. On Ramsey numbers of sparse graphs. Combin. Probab. Comput. 12 (2003) 627-641
15. Li Y., Rousseau C.C., and Soltés L. Ramsey linear families and generalized subdivided graphs. Discrete Math. (1997) 269-275
16. Nešetřil J. Ramsey Theory. In: Graham R.L., and Grötschel M. (Eds). Handbook of Combinatorics (1995), Elsevier 1331-1403
17. e s Journées Graphes et Algorithmes. LaBRI-Université Bordeaux I vol. 1372-05 (2005) 55-58
18. Nešetřil J., and Ossona de Mendez P. Grad and classes with bounded expansion I. Decompositions. European J. Combin. 29 3 (2008) 760-776
19. Nešetřil J., and Ossona de Mendez P. The grad of a graph and classes with bounded expansion. In: Raspaud A., and Delmas O. (Eds). 7th International Colloquium on Graph Theory. Electronic Notes in Discrete Mathematics vol. 22 (2005), Elsevier 101-106
20. J. Nešetřil, P. Ossona de Mendez, Linear time low tree-width partitions and algorithmic consequences, in: STOC'06 Proceedings of the 38th Annual ACM Symposium on Theory of Computing, 2006, pp. 391-400
21. Radziszowski S. Small Ramsey numbers. Electron. J. Comb. DS1 (2004). http://www.combinatorics.org/Surveys/ds1.pdf dynamic survey; http://www.combinatorics.org/Surveys/ds1.pdf
22. Rödl V., and Thomas R. Arrangeability and clique subdivisions. In: Graham R.L., and Nešetřil J. (Eds). The Mathematics of Paul Erdo{double acute}s (1991), Springer 236-239
23. L. Shi, Numbers and topologies: Two aspects of Ramsey theory, Ph.D. thesis, Mathematisch-Naturwissenschaftlichen Fakulta{double acute accent}t II, Humboldt-Universita{double acute accent}t zu Berlin, 2003
24. Shi L. Linear ramsey numbers of sparse graphs. J. Graph Theory 50 3 (2005) 175-185
25. Skrien D.J. A relationship between triangulated graphs comparability graphs, proper interval graphs, proper circular arc graphs, and nested interval graphs. J. Graph Theory 6 (1982) 309-316
26. E. Szemerédi, Colloquium at Emory University, Atlanta, GA, April 22, 1994