论文信息 - The Generation of Maximal Triangle-Free Graphs

The Generation of Maximal Triangle-Free Graphs

Abstract. In this paper we present an efficient algorithm for generating maximal triangle-free graphs. A program based on this algorithm has been used to check a conjecture of Erdo´´s about the local density of triangle-free graphs and turned out to be very powerful for the computation of triangle Ramsey numbers.

Stephan Brandt | Gunnar Brinkmann | Thomas Harmuth

[1] Kathrin Klamroth,et al. Ramsey numbers of K3 versus (p, q)-graphs , 1996, Ars Comb..

[2] Stephan Brandt,et al. The local density of triangle-free graphs , 1998, Discret. Math..

[3] Richard H. Schelp,et al. All triangle-graph ramsey numbers for connected graphs of order six , 1980, J. Graph Theory.

[4] Jeong Han Kim,et al. The Ramsey Number R(3, t) Has Order of Magnitude t2/log t , 1995, Random Struct. Algorithms.

[5] Gunnar Brinkmann,et al. All Ramsey Numbers r(K3, G) for Connected Graphs of Order 7 and 8 , 1998, Combinatorics, Probability and Computing.

[6] Xia Jin. Ramsey numbers involving a triangle: theory and algorithms , 1993 .

[7] Richard H. Schelp,et al. A local density condition for triangles , 1994, Discret. Math..

[8] D. West. Introduction to Graph Theory , 1995 .

[9] Brendan D. McKay,et al. Isomorph-Free Exhaustive Generation , 1998, J. Algorithms.

[10] Stephan Brandt,et al. All Ramsey numbers for connected graphs of order 9. , 1998 .

[11] Ingo Schiermeyer,et al. Ramsey Numbers r(K3, G) for Connected Graphs G of Order Seven , 1997, Discret. Appl. Math..