Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9514432 | Discrete Mathematics | 2018 | 8 Pages |
Abstract
Suppose that s, t are two positive integers, and â is a set of graphs. Let g(s,t;â) be the least integer g such that any â-free graph with minimum degree at least g can be partitioned into two sets which induced subgraphs have minimum degree at least s and t, respectively. For a given graph H, we simply write g(s,t;H) for g(s,t;â) when â={H}. In this paper, we show that if s,tâ¥2, then g(s,t;K2,3)â¤s+t and g(s,t;{K3,C8,K2,3})â¤s+tâ1. Moreover, if â is the set of graphs obtained by connecting a single vertex to exactly two vertices of K4âe, then g(s,t;â)â¤s+t on â-free graphs with at least five vertices, which generalize a result of Liu and Xu (2017).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jianfeng Hou, Huawen Ma, Jiguo Yu, Xia Zhang,