Tight binding number bound for P≥3-factor uniform graphs

Abstract

A graph G is P≥k-factor uniform if for arbitrary e1,e2∈E(G) with e1≠e2, G admits a P≥k-factor including e1 and excluding e2. Recently, Zhou and Sun [12] proved that a 2-edge-connected graph G is a P≥3-factor uniform graph if bind(G)>94. However, the maximum known binding number of a 2-edge-connected graph that is not P≥3-factor uniform is 5/3. In this paper, we prove that bind(G)>53 is exactly the tight binding number bound for P≥3-factor uniform graphs.