3-Paths in Graphs with Bounded Average Degree

Abstract

In this paper we study the existence of unavoidable paths on three vertices in sparse graphs. A path uvw on three vertices u, v, and w is of type (i, j, k) if the degree of u (respectively v, w) is at most i (respectively j, k). We prove that every graph with minimum degree at least 2 and average degree strictly less than m contains a path of one of the types

Keywords

• average degree
• structural property
• 3-path
• degree sequence