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Graph Decompositions Satisfying Extremal Degree Constraints

✍ Scribed by Paul A. Catlin

Publisher: John Wiley and Sons
Year: 1978
Tongue: English
Weight: 175 KB
Volume: 2
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190020210

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✦ Synopsis

Abstract

We show that the vertex set of any graph G with p⩾2 vertices can be partitioned into non‐empty sets V~1~, V~2~, such that the maximum degree of the induced subgraph 〈V~i~〉 does not exceed
where p^i^ = |V^i^|, for i=1, 2. Furthermore, the structure of the induced subgraphs is investigated in the extreme case.

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