TY - JOUR

T1 - Greedily constructing maximal partial f-factors

AU - Tankus, David

AU - Tarsi, Michael

PY - 2009/4/28

Y1 - 2009/4/28

N2 - 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.

AB - 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.

KW - Equimatchable

KW - Factors

KW - Greedy

KW - Hereditary system

UR - http://www.scopus.com/inward/record.url?scp=62849110175&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2008.04.047

DO - 10.1016/j.disc.2008.04.047

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AN - SCOPUS:62849110175

SN - 0012-365X

VL - 309

SP - 2180

EP - 2189

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 8

ER -