The ultimate categorical matching in a graph

The Ultimate Categorical Independence Ratio of a Graph

On the ultimate categorical independence ratio

Brown, Nowakowski and Rall defined the ultimate categorical independence ratio of a graph G as A(G) = lim k→∞ i(G×k), where i(G) = α(G) |V (G)| denotes the independence ratio of a graphG, andG ×k is the kth categorical power of G. Let a(G) = max{ |U | |U |+|NG(U)| : U is an independent set of G}, where NG(U) is the neighborhood of U in G. In this paper we answer a question of Alon and Lubetzky,...

Results on Independent Sets in Categorical Products of Graphs, the Ultimate Categorical Independence Ratio and the Ultimate Categorical Independent Domination Ratio

We show that there are polynomial-time algorithms to compute maximum independent sets in the categorical products of two cographs and two splitgraphs. The ultimate categorical independence ratio of a graph G is defined as limk→∞ α(G )/n. The ultimate categorical independence ratio is polynomial for cographs, permutation graphs, interval graphs, graphs of bounded treewidth and splitgraphs. When ...

ON THE MATCHING NUMBER OF AN UNCERTAIN GRAPH

Uncertain graphs are employed to describe graph models with indeterministicinformation that produced by human beings. This paper aims to study themaximum matching problem in uncertain graphs.The number of edges of a maximum matching in a graph is called matching numberof the graph. Due to the existence of uncertain edges, the matching number of an uncertain graph is essentially an uncertain var...

The Ultimate Categorical Independence Ratio of Complete Multipartite Graphs

The independence ratio i(G) of a graph G is the ratio of its independence number and the number of vertices. The ultimate categorical independence ratio of a graph G is defined as limk→∞ i(G×k), where G×k denotes the kth categorical power of G. This parameter was introduced by Brown, Nowakowski and Rall, who asked about its value for complete multipartite graphs. In this paper we determine the ...