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)

Longest cycles and independent sets in k-connected graphs

P. Fraisse, H. Jung

Recent Studies in Graph Theory,

1989

2 Excerpts

Longest paths and cycles in graphs with high degree, Research Report CORR 80-16

J. A. Bondy

Department of Combinatorics and Optimization,

1980

1 Excerpt

A note on Hamiltonian circuits

O. Ore

Amer. Math. Monthly

1960

1 Excerpt

Similar Papers

Loading similar papers…

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}
}