We first prove that for any fixed k a cubic graph with few short cycles contains a Kk-minor. This is a direct generalisation of a result on girth by Thomassen. We then use this the...
We study approximation algorithms, integrality gaps, and hardness of approximation, of two problems related to cycles of "small" length k in a given graph. The instance f...
Consider random regular graphs of order n and degree d = d(n) 3. Let g = g(n) 3 satisfy (d-1)2g-1 = o(n). Then the number of cycles of lengths up to g have a distribution simila...
Brendan D. McKay, Nicholas C. Wormald, Beata Wysoc...
: Let G be a toroidal graph without cycles of a fixed length k, and l(G) the list chromatic number of G. We establish tight upper bounds Contract grant sponsor: RGC; Contract grant...