Displaying similar documents to “On k-factor-critical graphs”

Forbidden Structures for Planar Perfect Consecutively Colourable Graphs

Marta Borowiecka-Olszewska, Ewa Drgas-Burchardt (2017)

Discussiones Mathematicae Graph Theory

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A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose...

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.

Total domination edge critical graphs with maximum diameter

Lucas C. van der Merwe, Cristine M. Mynhardt, Teresa W. Haynes (2001)

Discussiones Mathematicae Graph Theory

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Denote the total domination number of a graph G by γₜ(G). A graph G is said to be total domination edge critical, or simply γₜ-critical, if γₜ(G+e) < γₜ(G) for each edge e ∈ E(G̅). For 3ₜ-critical graphs G, that is, γₜ-critical graphs with γₜ(G) = 3, the diameter of G is either 2 or 3. We characterise the 3ₜ-critical graphs G with diam G = 3.

Erdős regular graphs of even degree

Andrey A. Dobrynin, Leonid S. Mel&amp;#039;nikov, Artem V. Pyatkin (2007)

Discussiones Mathematicae Graph Theory

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In 1960, Dirac put forward the conjecture that r-connected 4-critical graphs exist for every r ≥ 3. In 1989, Erdös conjectured that for every r ≥ 3 there exist r-regular 4-critical graphs. A method for finding r-regular 4-critical graphs and the numbers of such graphs for r ≤ 10 have been reported in [6,7]. Results of a computer search for graphs of degree r = 12,14,16 are presented. All the graphs found are both r-regular and r-connected.

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].

A characterization of diameter-2-critical graphs with no antihole of length four

Teresa Haynes, Michael Henning (2012)

Open Mathematics

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A graph G is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. In this paper we characterize the diameter-2-critical graphs with no antihole of length four, that is, the diameter-2-critical graphs whose complements have no induced 4-cycle. Murty and Simon conjectured that the number of edges in a diameter-2-critical graph of order n is at most n 2/4 and that the extremal graphs are complete bipartite graphs with equal size partite sets. As...

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...

Magic and supermagic dense bipartite graphs

Jaroslav Ivanco (2007)

Discussiones Mathematicae Graph Theory

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A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.

Factor-criticality and matching extension in DCT-graphs

Odile Favaron, Evelyne Favaron, Zdenĕk Ryjáček (1997)

Discussiones Mathematicae Graph Theory

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The class of DCT-graphs is a common generalization of the classes of almost claw-free and quasi claw-free graphs. We prove that every even (2p+1)-connected DCT-graph G is p-extendable, i.e., every set of p independent edges of G is contained in a perfect matching of G. This result is obtained as a corollary of a stronger result concerning factor-criticality of DCT-graphs.