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Counterexamples to two conjectures of Hilton

✍ Scribed by S. Fiorini

Publisher
John Wiley and Sons
Year
1978
Tongue
English
Weight
122 KB
Volume
2
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

Counterexamples are presented to the following two conjectures of Hilton:

A graph which does not contain a spanning K~1t~ is Vl‐critical if and only if it is VC‐critical.

If G is a class‐two graph which contains a spanning Pl‐critical subgraph H of the same chromatic index as G, then G is Vl‐critical.

The counterexample to the second conjecture also illustrates that a class‐two graph can have distinct Pl‐critical subgraphs.

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