๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the characterization of path graphs

โœ Scribed by Huaien Li; Yixun Lin


Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
191 KB
Volume
17
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

โœฆ Synopsis


Abstract

Broersma and Hoede have introduced path graphs. Their characterization of P~3~โ€graphs contains a flaw. This note presents the correct form of the characterization. ยฉ 1993 John Wiley & Sons, Inc.


๐Ÿ“œ SIMILAR VOLUMES


On the hamiltonian path graph of a graph
โœ George R. T. Hendry ๐Ÿ“‚ Article ๐Ÿ“… 1987 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 491 KB ๐Ÿ‘ 1 views

The hamiltonian path graph H(F) of a graph F is that graph having the same vertex set as F and in which two vertices u and u are adjacent if and only if F contains a hamiltonian u -u path. First, in response to a conjecture of Chartrand, Kapoor and Nordhaus, a characterization of nonhamiltonian grap

On Path-amenable Graphs
โœ Gabriel Dirac; Ove Steen Nielsen ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 373 KB
A characterization of graphs without lon
โœ Gรกbor Bacsรณ; Zsolt Tuza ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 461 KB ๐Ÿ‘ 1 views

## Abstract In a connected graph define the kโ€center as the set of vertices whose distance from any other vertex is at most __k.__ We say that a vertex set __S__ __d__โ€dominates __G__ if for every vertex x there is a y โˆˆ __S__ whose distance from __x__ is at most __d__. Call a graph __P~t~__โ€free

Characterizing directed path graphs by f
โœ Kathie Cameron; Chรญnh T. Hoร ng; Benjamin Lรฉvรชque ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 135 KB

An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. Asteroidal triples play a central role in a classical characterization of interval graphs by Lekkerkerker and Boland. Their result says that a chordal grap

Characterizing path graphs by forbidden
โœ Benjamin Lรฉvรชque; Frรฉdรฉric Maffray; Myriam Preissmann ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 197 KB

## Abstract A path graph is the intersection graph of subpaths of a tree. In 1970, Renz asked for a characterization of path graphs by forbidden induced subgraphs. We answer this question by determining the complete list of graphs that are not path graphs and are minimal with this property. ยฉ 2009

On paths in planar graphs
โœ Sanders, Daniel P. ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 93 KB ๐Ÿ‘ 2 views

This paper generalizes a theorem of Thomassen on paths in planar graphs. As a corollary, it is shown that every 4-connected planar graph has a Hamilton path between any two specified vertices x, y and containing any specified edge other than xy.