A good characterization of cograph contractions

Lê, Van Bang

doi:10.1002/(sici)1097-0118(199904)30:4<309::aid-jgt5>3.0.co;2-5

Cited by 4 publications

(1 citation statement)

References 9 publications

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“…One of the interesting cases is the class G of P 4 -free graphs (cographs). Recently, Van Bang Le [141] described G * for them. It follows, in particular, that the membership in this class can be decided in polynomial time.…”

Section: Good Characterizationsmentioning

confidence: 99%

Graph colorings with local constraints -- a survey

Tuza¹

1997

Discuss. Math. Graph Theory

220

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We survey the literature on those variants of the chromatic number problem where not only a proper coloring has to be found (i.e., adjacent vertices must not receive the same color) but some further local restrictions are imposed on the color assignment. Mostly, the list colorings and the precoloring extensions are considered. In one of the most general formulations, a graph G = (V, E), sets L(v) of admissible colors, and natural numbers c v for the vertices v ∈ V are given, and the question is whether there can be chosen a subset C(v) ⊆ L(v) of cardinality c v for each vertex in such a way that the sets C(v), C(v) are disjoint for each pair v, v of adjacent vertices. The particular case of constant |L(v)| with c v = 1 for all v ∈ V leads to the concept of choice number, a graph parameter showing unexpectedly different behavior compared to the chromatic number, despite these two invariants have nearly the same value for almost all graphs. To illustrate typical techniques, some of the proofs are sketched.

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Section: Good Characterizationsmentioning

confidence: 99%

Graph colorings with local constraints -- a survey

Tuza¹

1997

Discuss. Math. Graph Theory

220

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Forbidden induced subgraph characterization of cograph contractions

Zverovich

2004

Journal of Graph Theory

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Let S 1 ; S 2 ; . . . ; S t be pairwise disjoint non-empty stable sets in a graph H. The graph H Ã is obtained from H by: (i) replacing each S i by a new vertex q i ; (ii) joining each q i and q j , 1 i 6 ¼ j t, and; (iii) joining q i to all vertices in HÀ(S 1 [ S 2 [ Á Á Á [ S t ) which were adjacent to some vertex of S i . A cograph is a P 4 -free graph. A graph G is called a cograph contraction if there exist a cograph H and pairwise disjoint non-empty stable sets in H for which G ' H Ã . Solving a problem proposed by Le [2], we give a finite forbidden induced subgraph characterization of cograph contractions.

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Characterisations and Linear-Time Recognition of Probe Cographs

Lê

Ridder

2007

Graph-Theoretic Concepts in Computer Science

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A good characterization of cograph contractions

Cited by 4 publications

References 9 publications

Graph colorings with local constraints -- a survey

Graph colorings with local constraints -- a survey

Forbidden induced subgraph characterization of cograph contractions

Characterisations and Linear-Time Recognition of Probe Cographs

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