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Biclosure and bistability in a balanced bipartite graph
Author(s) -
Amar Denise,
Favaron Odile,
Mago Pedro,
Ordaz Oscar
Publication year - 1995
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.3190200414
Subject(s) - bipartite graph , combinatorics , mathematics , graph , bistability , degree (music) , discrete mathematics , edge transitive graph , property (philosophy) , order (exchange) , graph power , line graph , physics , quantum mechanics , philosophy , epistemology , finance , acoustics , economics
The k ‐biclosure of a balanced bipartite graph wiht color classes A and B is the graph obtained from G by recursively joining pairs of nonadjacent vertices respectively taken in A and B whose degree sum is at least k , until no such pair remains. A property P defined on all the balanced bipartite graphs of order 2 n is k ‐bistable if whenever G + ab has property P and d G ( b ) ≧ k then G itself has property P . We present a synthesis of results involving, for some properties, P , the bistability of P , the k ‐biclosure of G , the number of edges and the minimum degree. © 1995 John Wiley & Sons, Inc.