Abstract
For a graph G and a family of graphs F, the general Kneser graph KG(G,F) is a graph with the vertex set consisting of all subgraphs of G isomorphic to some member of F and two vertices are adjacent if their corresponding subgraphs are edge disjoint. In this paper, we introduce some generalizations of Turán number of graphs. In view of these generalizations, we give some lower and upper bounds for the chromatic number of general Kneser graphs KG(G,F). Using these bounds, we determine the chromatic number of some family of general Kneser graphs KG(G,F) in terms of generalized Turán number of graphs. In particular, we determine the chromatic number of every Kneser multigraph KG(G,F) where G is a multigraph each of whose edges has the multiplicity at least 2 and F is an arbitrary family of simple graphs. Moreover, the chromatic number of general Kneser graph KG(G,F) is exactly determined where G is a dense graph and F={K1,2}.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.