Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4949617 | Discrete Applied Mathematics | 2017 | 7 Pages |
Abstract
Let s,t be two integers, and let g(s,t) denote the minimum integer such that the vertex set of a graph of minimum degree at least g(s,t) can be partitioned into two nonempty sets which induce subgraphs of minimum degree at least s and t, respectively. In this paper, it is shown that, (1) for positive integers s and t, g(s,t)â¤s+t on (K4âe)-free graphs except K3, and (2) for integers sâ¥2 and tâ¥2, g(s,t)â¤s+tâ1 on triangle-free graphs in which no two quadrilaterals share edges. Our first conclusion generalizes a result of Kaneko (1998), and the second generalizes a result of Diwan (2000).
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Muhuo Liu, Baogang Xu,