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Graph partitions with minimum degree constraints

✍ Scribed by Esther M. Arkin; Refael Hassin

Book ID: 104114141
Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 388 KB
Volume: 190
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00114-9

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✦ Synopsis

Given a graph with n nodes and minimum degree 6, we give a polynomial time algorithm that constructs a partition of the nodes of the graph into two sets X and Y such that the sum of the minimum degrees in X and in Y is at least 6 and the cardinalities of X and Y differ by at most 6 (6 + 1 if n ~ 6 (rood 2)). The existence of such a partition was shown by Sheehan (1988). (~

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## Abstract For each pair __s,t__ of natural numbers there exist natural numbers __f(s,t)__ and __g(s,t)__ such that the vertex set of each graph of connectivity at least __f(s,t)__ (respectively minimum degree at least __g(s,t))__ has a decomposition into sets which induce subgraphs of connectivit