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Chromatic numbers of hypergraphs and coverings of graphs
Author(s) -
Miller Zevi,
Müller Heinrich
Publication year - 1981
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190050311
Subject(s) - mathematics , combinatorics , chromatic scale , disjoint sets , generalization , graph , discrete mathematics , disjoint union (topology) , mathematical analysis
Burr recently proved [3] that for positive integers m 1 , m 2 …… m k , and any graph G we have X(G)\documentclass{article}\pagestyle{empty}\begin{document}$ \chi (G)\, \le \,\mathop \prod \limits_{i = 1}^k m_i $\end{document}if and only if G can be expressed as the edge disjoint union of subgraphs F i satisfying X(F i ) ≤ m i . This theorem is generalized to hypergraphs. By suitable interpretations the generalization is then used to deduce propositions on coverings of graphs.