: 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...
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...
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...