Relationships between the length of a longest path and the relative length

Abstract

Let G be a graph, and let p(G) and c(G) be the order of a longest path and a longest cycle of G, respectively. In [J. Graph Theory 30 (1999), 91– 99], Saito proved that if G is a 2-connected graph with p(G)− c(G) ≥ 2, then p(G) ≥ σ3(G) − 1. In this paper, we evaluate the length of a longest path of G by using σ4(G). Specifically, our main results are the… (More)

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Cite this paper

@article{Chiba2010RelationshipsBT, title={Relationships between the length of a longest path and the relative length}, author={Shuya Chiba and Ryota Matsubara and Masao Tsugaki}, journal={Australasian J. Combinatorics}, year={2010}, volume={47}, pages={91-108} }