Greedily constructing maximal partial f -factors

Let G = ( V , E ) be a graph and let f be a function f : V → N . A partial f -factor of G is a subgraph H of G , such that the degree in H of every vertex v ∈ V is at most f ( v ) . We study here the recognition problem of graphs, where all maximal partial f -factors have the same number of edges. G...

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Bibliographic Details
Published inDiscrete mathematics Vol. 309; no. 8; pp. 2180 - 2189
Main Authors Tankus, David, Tarsi, Michael
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 28.04.2009
Elsevier
Subjects
Applied sciences
Computer science; control theory; systems
Equimatchable
Exact sciences and technology
Factors
Greedy
Hereditary system
Information retrieval. Graph
Theoretical computing
Equimatchable
Hereditary system
Greedy
Factors
Characterization
Vertex
Subgraph
Maximal graph
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Summary:Let G = ( V , E ) be a graph and let f be a function f : V → N . A partial f -factor of G is a subgraph H of G , such that the degree in H of every vertex v ∈ V is at most f ( v ) . We study here the recognition problem of graphs, where all maximal partial f -factors have the same number of edges. Graphs which satisfy that property for the function f ( v ) ≡ 1 are known as equimatchable and their recognition problem is the subject of several previous articles in the literature. We show the problem is polynomially solvable if the function f is bounded by a constant, and provide a structural characterization for graphs with girth at least 5 in which all maximal partial 2-factors are of the same size.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2008.04.047