Fractional perfect b-matching polytopes I: General theory

Behrend, Roger E. ORCID: https://orcid.org/0000-0002-6143-7439 2013. Fractional perfect b-matching polytopes I: General theory. Linear Algebra and its Applications 439 (12) , pp. 3822-3858. 10.1016/j.laa.2013.10.001

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Abstract

The fractional perfect b-matching polytope of an undirected graph G is the polytope of all assignments of nonnegative real numbers to the edges of G such that the sum of the numbers over all edges incident to any vertex v is a prescribed nonnegative number b_v. General theorems which provide conditions for nonemptiness, give a formula for the dimension, and characterize the vertices, edges and face lattices of such polytopes are obtained. Many of these results are expressed in terms of certain spanning subgraphs of G which are associated with subsets or elements of the polytope. For example, it is shown that an element u of the fractional perfect b-matching polytope of G is a vertex of the polytope if and only if each component of the graph of u either is acyclic or else contains exactly one cycle with that cycle having odd length, where the graph of u is defined to be the spanning subgraph of G whose edges are those at which u is positive.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	graphs; polytope; perfect matching
Additional Information:	Online publication date: 25 October 2013.
Publisher:	Elsevier
ISSN:	0024-3795
Date of First Compliant Deposit:	30 March 2016
Last Modified:	16 May 2023 16:05
URI:	https://orca.cardiff.ac.uk/id/eprint/43147

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