SIAMDM
2008
13 years 11 months ago
2008
We show that every triangle-free graph on the double torus is 4-colorable. This settles a problem raised by Gimbel and Thomassen [Trans. Amer. Math. Soc. 349 (1997), 4555
JCT
2006
13 years 11 months ago
2006
One of Erdos' favourite conjectures was that any triangle-free graph G on n vertices should contain a set of n/2 vertices that spans at most n2/50 edges. We prove this when t...
DAM
2006
13 years 11 months ago
2006
We prove that a triangle-free graph G is a tolerance graph if and only if there exists a set of consecutively ordered stars that partition the edges of G. Since tolerance graphs a...