Results 21 to 30 of about 3,613,364 (137)
Some Variations of Perfect Graphs
Discussiones Mathematicae Graph Theory, 2016 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.
Dettlaff Magda +3 more
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Graph Classes Generated by Mycielskians
Discussiones Mathematicae Graph Theory, 2020 In this paper we use the classical notion of weak Mycielskian M′(G) of a graph G and the following sequence: M′0(G) = G, M′1(G) = M′(G), and M′n(G) = M′(M′n−1(G)), to show that if G is a complete graph of order p, then the above sequence is a generator ...
Borowiecki Mieczys law +3 more
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Theory and Applications of GraphsA class G of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by G^{apex} the class of graphs G that contain a vertex v such that G − v is in G.
Jagdeep Singh +2 more
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Forbidden induced subgraph of the Comparability Graph and Three Colored Posets
, 2018 The cover-incomparability graph of a poset P is the edge-union of the covering and the incomparability graph of P. As a continuation of the study of 3-colored diagrams we characterize some forbidden ⊲ - preserving subposets of the posets whose cover ...
Sibi C Babu, Baiju Sukumaran, Athul T B
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Characterizing the forbidden pairs for graphs to be super-edge-connected
AKCE International Journal of Graphs and CombinatoricsLet [Formula: see text] be a set of given connected graphs. A graph G is said to be [Formula: see text]-free if G contains no H as an induced subgraph for any [Formula: see text].
Hazhe Ye, Yingzhi Tian
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An induced subgraph characterization of domination perfect graphs [PDF]
, 1995 Let γ(G) ι(G) be the domination number and independent domination number of a graph (G), respectively. A graph (G) is called domination perfect if γ(H) = ι(H), for every induced subgraph H of (G).
Vadim E. Zverovich +5 more
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Characterizing heavy subgraph pairs for pancyclicity [PDF]
, 2015 Earlier results originating from Bedrossian’s PhD Thesis focus on characterizing pairs of forbidden subgraphs that imply hamiltonian properties. Instead of forbidding certain induced subgraphs, here we relax the requirements by imposing Ore-type degree ...
Broersma, Hajo; id_orcid +3 more
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Toughness, Forbidden Subgraphs and Pancyclicity [PDF]
, 2021 Motivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion
Broersma, Hajo; id_orcid +5 more
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Line Graphs of Multigraphs and the Forbidden Graph E 6
Journal of Graph Theory, EarlyView.ABSTRACT The line graph Γ of a multigraph Δ is the graph whose vertices are the edges of Δ, where two such edges are adjacent if and only if they meet in a single vertex of Δ. We provide several characterizations of such line graphs and in particular show that a graph is a line graph if and only if it does not contain one of the 32 graphs, all of which
Hans Cuypers
wiley +1 more source
Small clique number graphs with three trivial critical ideals
Special Matrices, 2018 The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. Previously, they have been used in the understanding and characterizing of the graphs with critical group with few invariant factors ...
Alfaro Carlos A., Valencia Carlos E.
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