Counterexamples to two conjectures of Hilton
Stanley Fiorini · Journal of Graph Theory · 1978
Abstract Counterexamples are presented to the following two conjectures of Hilton: A graph which does not contain a spanning K1t 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.