论文信息 - The Ramsey numbers for cycles versus wheels of even order

The Ramsey numbers for cycles versus wheels of even order

For two given graphs G"1 and G"2, the Ramsey number R(G"1,G"2) is the smallest integer n such that for any graph G of order n, either G contains G"1 or the complement of G contains G"2. Let C"n denote a cycle of order n and W"m a wheel of order m+1. Surahmat, Baskoro and Tomescu conjectured that R(C"n,W"m)=3n-2 for m odd, n>=m>=3 and (n,m) (3,3). In this paper, we confirm the conjecture for n>=20.

T. C. Edwin Cheng | Lianmin Zhang | Yaojun Chen

[1] Rainer Bodendiek,et al. Topics In Combinatorics and Graph Theory , 1992 .

[2] G. Dirac. Some Theorems on Abstract Graphs , 1952 .

[3] H. A. Jung. Long Cycles in Graphs with Moderate Connectivity , 1990 .

[4] Yunqing Zhang,et al. The Ramsey numbers of stars versus wheels , 2004, Eur. J. Comb..

[5] V. Rosta. On a ramsey-type problem of J. A. Bondy and P. Erdös. I , 1973 .

[6] Edy Tri Baskoro,et al. The Ramsey numbers of large cycles versus wheels , 2006, Discret. Math..

[7] Edy Tri Baskoro,et al. The Ramsey numbers of large cycles versus small wheels , 2002 .

[8] Odile Favaron,et al. Independence and hamiltonicity in 3-domination-critical graphs , 1997 .

[9] S. Radziszowski. Small Ramsey Numbers , 2011 .

[10] Edy Tri Baskoro,et al. The Ramsey Numbers of Large cycles Versus Odd Wheels , 2008, Graphs Comb..

[11] Vasek Chvátal,et al. Tree-complete graph ramsey numbers , 1977, J. Graph Theory.

[12] Richard H. Schelp,et al. All Ramsey numbers for cycles in graphs , 1974, Discret. Math..

[13] Yunqing Zhang,et al. The Ramsey numbers of paths versus wheels , 2005, Discret. Math..