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1996 | 16 | 2 | 173-179
Tytuł artykułu

Remarks on 15-vertex (3,3)-ramsey graphs not containing K₅

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper gives an account of previous and recent attempts to determine the order of a smallest graph not containing K₅ and such that every 2-coloring of its edges results in a monochromatic triangle. A new 14-vertex K₄-free graph with the same Ramsey property in the vertex coloring case is found. This yields a new construction of one of the only two known 15-vertex (3,3)-Ramsey graphs not containing K₅.
Wydawca
Rocznik
Tom
16
Numer
2
Strony
173-179
Opis fizyczny
Daty
wydano
1996
otrzymano
1996-07-27
poprawiono
1996-11-18
Twórcy
  • Department of Discrete Mathematics, Faculty of Mathematics and Computer Science, Adam Mickiewicz University Poznań, Poland
Bibliografia
  • [1] J. Bukor, A note on the Folkman number F(3,3;5), Math. Slovaca 44 (1994) 479-480.
  • [2] P. Erdős and A. Hajnal, Research problem 2-5, J. Combin. Theory 2 (1967) 104.
  • [3] M. Erickson, An upper bound for the Folkman number F(3,3;5), J. Graph Theory 17 (1993) 679-681, doi: 10.1002/jgt.3190170604.
  • [4] J. Folkman, Graphs with monochromatic complete subgraphs in every edge coloring, SIAM J. Appl. Math. 18 (1970) 19-24, doi: 10.1137/0118004.
  • [5] P. Frankl and V. Rödl, Large triangle-free subgraphs in graphs without K₄, Graphs and Combinatorics 2 (1986) 135-144, doi: 10.1007/BF01788087.
  • [6] R.L. Graham, On edgewise 2-colored graphs with monochromatic triangles and containing no complete hexagon, J. Combin. Theory 4 (1968) 300, doi: 10.1016/S0021-9800(68)80009-2.
  • [7] R.L. Graham and J.H. Spencer, On small graphs with forced monochromatic triangles, in: Recent Trends in Graph Theory. Lecture Notes in Math. 186 (Springer-Verlag, Berlin, 1971) 137-141, doi: 10.1007/BFb0059431.
  • [8] N. Hadziivanov and N. Nenov, On Graham-Spencer number, C.R. Acad. Bulg. Sci. 32 (1979) 155-158.
  • [9] N. Hadziivanov and N. Nenov, On Ramsey graphs, God. Sofij. Univ. Fak. Mat. Mech. 78 (1984) 211-214.
  • [10] N. Hadziivanov and N. Nenov, Every (3,3)-Ramsey graph without 5-cliques has more than 11 vertices, Serdica 11 (1985) 341-356.
  • [11] R.W. Irving, On a bound of Graham and Spencer for graph-coloring constant, J. Combin. Theory 15 (1973) 200-203, doi: 10.1016/0095-8956(73)90021-X.
  • [12] S. Lin, On Ramsey numbers and $K_r$-coloring of graphs, J. Combin. Theory (B) 12 (1972) 82-92, doi: 10.1016/0095-8956(72)90034-2.
  • [13] N. Nenov, New lower bound for Graham-Spencer number, Serdica 6 (1980) 373-383.
  • [14] N. Nenov, An example of 15-vertex (3,3)-Ramsey graph with the clique number 4, C.R. Acad. Bulg. Sci. 34 (1981) 1487-1489.
  • [15] M. Schauble, Zu einem Kantenfarbungsproblem, Wiss. Z. Th. Ilemenau 15 (1969) 55-58.
  • [16] J. Spencer, Three hundred million points suffice, J. Combin. Theory (A) 49 (1988) 210-217. See erratum in 50 p. 323.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1032
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