Some sufficient conditions for the existence of a 1‐factor | Zendy

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Some sufficient conditions for the existence of a 1‐factor

Author(s) -

Nebeský Ladislav

Publication year - 1978

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.3190020308

Subject(s) - mathematics , combinatorics , lemma (botany) , induced subgraph isomorphism problem , induced subgraph , graph , graph factorization , order (exchange) , discrete mathematics , graph power , line graph , voltage graph , vertex (graph theory) , ecology , poaceae , finance , economics , biology

The following theorem is proved: Let G be a graph of even order. Assume that there exists a connected spanning subgraph F of G such that for every set U of four vertices in G , if the subgraph of F induced by U is a star, then the subgraph of G induced by U is complete. Then G has a 1‐factor. The above theorem is derived from another sufficient condition for the existence of a 1‐factor, which is also proved in this paper (Lemma 1).

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