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Graph Decompositions without Isolated Vertices

โœ Scribed by H. Enomoto

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
405 KB
Volume
63
Category
Article
ISSN
0095-8956

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โœฆ Synopsis

We prove the following conjecture of A. Frank (Fifth British Combinatorial Conference, Aberdeen, Scotland, 1975): Let (G) be a connected simple graph of order (n), and (n=n_{1}+\cdots+n_{k}) be a partition of (n) with (n_{i} \geqslant 2). Suppose that the minimum degree of (G) is at least (k). Then the vertex set (V(G)) can be decomposed into disjoint subsets (V_{1}, \ldots, V_{k}) so that (\left|V_{i}\right|=n_{i}) and the subgraph induced by (V_{i}) contains no isolated vertices for all (i, 1 \leqslant i \leqslant k . \quad 1,1995) Academic Press, Inc.

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