𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Relative Length of Longest Paths and Cycles in Graphs

✍ Scribed by Huiqing Liu; Mei Lu; Feng Tian


Publisher
Springer Japan
Year
2007
Tongue
English
Weight
120 KB
Volume
23
Category
Article
ISSN
0911-0119

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


Relative length of longest paths and cyc
✍ Rao Li; Akira Saito; R.H. Schelp πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 184 KB πŸ‘ 2 views

## Abstract For a graph __G__, let __p(G)__ denote the order of a longest path in __G__ and __c(G)__ the order of a longest cycle in __G__, respectively. We show that if __G__ is a 3‐connected graph of order __n__ such that $\textstyle{\sum^{4}\_{i=1}\,{\rm deg}\_{G}\,x\_{i} \ge {3\over2}\,n + 1}$

On relative length of longest paths and
✍ Kenta Ozeki; Masao Tsugaki; Tomoki Yamashita πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 144 KB πŸ‘ 1 views

## Abstract For a graph __G__, __p__(__G__) and __c__(__G__) denote the order of a longest path and a longest cycle of __G__, respectively. In this paper, we prove that if __G__ is a 3 ‐connected graph of order __n__ such that the minimum degree sum of four independent vertices is at least __n__+ 6

Longest paths and cycles in bipartite or
✍ Zhang Ke Min πŸ“‚ Article πŸ“… 1987 πŸ› John Wiley and Sons 🌐 English βš– 430 KB πŸ‘ 1 views

In this paper we obtain two sufficient conditions, Ore type (Theorem 1) and Dirac type (Theorem 2). on the degrees of a bipartite oriented graph for ensuring the existence of long paths and cycles. These conditions are shown to be the best possible in a sense. An oriented graph is a digraph without

Longest paths and cycles in K1,3-free gr
✍ Manton M. Matthews; David P. Sumner πŸ“‚ Article πŸ“… 1985 πŸ› John Wiley and Sons 🌐 English βš– 383 KB πŸ‘ 2 views

In this article w e show that the standard results concerning longest paths and cycles in graphs can be improved for K,,,-free graphs. We obtain as a consequence of these results conditions for the existence of a hamiltonian path and cycle in K,,,-free graphs.