Displaying similar documents to “On a perfect problem”

Mycielskians and matchings

Tomislav Doslić (2005)

Discussiones Mathematicae Graph Theory

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It is shown in this note that some matching-related properties of graphs, such as their factor-criticality, regularizability and the existence of perfect 2-matchings, are preserved when iterating Mycielski's construction.

Comparing imperfection ratio and imperfection index for graph classes

Arie M. C. A. Koster, Annegret K. Wagler (2008)

RAIRO - Operations Research - Recherche Opérationnelle

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Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations with respect to different concepts. Perfect graphs are, for instance, precisely those graphs G where the stable set polytope STAB ( G ) coincides with the fractional stable set polytope QSTAB ( G ) . For all imperfect graphs G it holds that STAB ( G ) ⊂ QSTAB ( G ) . It is, therefore, natural to use the difference between the two polytopes in order to decide how far an imperfect graph is away from being perfect. We discuss...

Distance perfectness of graphs

Andrzej Włoch (1999)

Discussiones Mathematicae Graph Theory

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In this paper, we propose a generalization of well known kinds of perfectness of graphs in terms of distances between vertices. We introduce generalizations of α-perfect, χ-perfect, strongly perfect graphs and we establish the relations between them. Moreover, we give sufficient conditions for graphs to be perfect in generalized sense. Other generalizations of perfectness are given in papers [3] and [7].

Some Variations of Perfect Graphs

Magda Dettlaff, Magdalena Lemańska, Gabriel Semanišin, Rita Zuazua (2016)

Discussiones Mathematicae Graph Theory

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We consider (ψk−γk−1)-perfect graphs, i.e., graphs G for which ψk(H) = γk−1(H) for any induced subgraph H of G, where ψk and γk−1 are the k-path vertex cover number and the distance (k − 1)-domination number, respectively. We study (ψk−γk−1)-perfect paths, cycles and complete graphs for k ≥ 2. Moreover, we provide a complete characterisation of (ψ2 − γ1)- perfect graphs describing the set of its forbidden induced subgraphs and providing the explicit characterisation of the structure...

A note on pm-compact bipartite graphs

Jinfeng Liu, Xiumei Wang (2014)

Discussiones Mathematicae Graph Theory

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A graph is called perfect matching compact (briefly, PM-compact), if its perfect matching graph is complete. Matching-covered PM-compact bipartite graphs have been characterized. In this paper, we show that any PM-compact bipartite graph G with δ (G) ≥ 2 has an ear decomposition such that each graph in the decomposition sequence is also PM-compact, which implies that G is matching-covered