Time and place: 15:00 Monday 16 November in Monadelphous DS
Speaker: Reza Naserasr (Université Paris-Sud)
Title: Bounding K_4-minor-free graphs in the homomorphism order
Abstract: Given a graph B of odd-girth 2k+1 we are interested in the following question: Does every K_4-minor-free graph of odd-girth at least 2k+1 admit a homomorphism to B? We present a necessary and sufficient condition for B to minimally be a yes instance. Using this, we present a polynomial time algorithm (in the order of B) to answer the question for a given B. We then turn our focus on finding smallest order of YES-instances. We provide a few families of them, relating the question to a conjecture in extension of the 4CT and to fractional and circular chromatic number of K_4-minor-free graphs of odd-girth 2k+1. Finally we present an application to edge-coloring of regular K_4-minor-free plane graphs.
Joint work with: L. Beaudou, F. Foucaud and Q. Sen
Speaker: Reza Naserasr (Université Paris-Sud)
Title: Bounding K_4-minor-free graphs in the homomorphism order
Abstract: Given a graph B of odd-girth 2k+1 we are interested in the following question: Does every K_4-minor-free graph of odd-girth at least 2k+1 admit a homomorphism to B? We present a necessary and sufficient condition for B to minimally be a yes instance. Using this, we present a polynomial time algorithm (in the order of B) to answer the question for a given B. We then turn our focus on finding smallest order of YES-instances. We provide a few families of them, relating the question to a conjecture in extension of the 4CT and to fractional and circular chromatic number of K_4-minor-free graphs of odd-girth 2k+1. Finally we present an application to edge-coloring of regular K_4-minor-free plane graphs.
Joint work with: L. Beaudou, F. Foucaud and Q. Sen