Title

Uniquely partitionable graphs

Abstract

A graph is /-degenerate if it does not contain a subgraph whose minimum degree is greater than l. A (k, l)-partition of a graph G is a partition of the vertex set V(G) of G into k subsets V1,., Vksuch that each Vtinduces an l-degenerate graph. A graph with exactly one (k, l)-partition is said to be uniquely (k, l)-partitionable. Extending a number of earlier results, we prove that for every k,/and g there are non-trivial uniquely (k, l)-partitionable graphs of girth at least g. © 1977, Oxford University Press.

Publication Title

Journal of the London Mathematical Society

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