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The isodominism class of the graphs
Discrete Mathematics, Algorithms and Applications, 2020In this paper, the new concept [Formula: see text]-isodominism between two graphs is introduced, where [Formula: see text] is a positive integer. The [Formula: see text]-isodominism is a pair of the graph isomorphism which depends on the smallest [Formula: see text]-dominating sets.
Behnaz Tolue, Amin Rafiei
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Journal of Computer and System Sciences, 2023 Let $\Pi$ be a hereditary graph class. The problem of deletion to $\Pi$, takes as input a graph $G$ and asks for a minimum number (or a fixed integer $k$) of vertices to be deleted from $G$ so that the resulting graph belongs to $\Pi$.
Venkaṭesh Raman +2 more
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Arrangement graphs: a class of generalized star graphs
Information Processing Letters, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Khaled Day, Anand R. Tripathi
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Journal of Graph Theory, 2006
AbstractIn this article we introduce certain classes of graphs that generalize ϕ‐tolerance chain graphs. In a rank‐tolerance representation of a graph, each vertex is assigned two parameters: a rank, which represents the size of that vertex, and a tolerance which represents an allowed extent of conflict with other vertices. Two vertices are adjacent if
Martin Charles Golumbic +1 more
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AbstractIn this article we introduce certain classes of graphs that generalize ϕ‐tolerance chain graphs. In a rank‐tolerance representation of a graph, each vertex is assigned two parameters: a rank, which represents the size of that vertex, and a tolerance which represents an allowed extent of conflict with other vertices. Two vertices are adjacent if
Martin Charles Golumbic +1 more
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Intersection Dimensions of Graph Classes
Graphs and Combinatorics, 1994``The intersection dimension of a graph \(G\) with respect to a class \(A\) of graphs is the minimum \(k\) such that \(G\) is the intersection of at most \(k\) graphs on vertex set \(V(G)\) each of which belongs to \(A\). We consider the question when the intersection dimension of a certain family of graphs is bounded or unbounded.'' If \(A\) is ...
Jan Kratochvíl, Zsolt Tuza
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SIAM Journal on Algebraic Discrete Methods, 1982
Let P be a simply connected polyomino. Let $G( P )$ be the graph whose vertices are the maximal rectangles in P, two such vertices being adjacent if the corresponding rectangles have nontrivial intersection. In this paper we show that $G ( P )$ is perfect. This solves a problem posed by Berge et al.
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Let P be a simply connected polyomino. Let $G( P )$ be the graph whose vertices are the maximal rectangles in P, two such vertices being adjacent if the corresponding rectangles have nontrivial intersection. In this paper we show that $G ( P )$ is perfect. This solves a problem posed by Berge et al.
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Properties of Classes of Random Graphs
Combinatorics, Probability and Computing, 1994In [11] it is shown that the theory of almost all graphs is first-order complete. Furthermore, in [3] a collection of first-order axioms are given from which any first-order property or its negation can be deduced. Here we show that almost all Steinhaus graphs satisfy the axioms of almost all graphs and conclude that a first-order property is true for ...
Neal Brand, Steve Jackson 0001
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2018
This edited volume offers a detailed account on the theory of directed graphs from the perspective of important classes of digraphs, with each chapter written by experts on the topic.Outlining fundamental discoveries and new results obtained over recent years, this book provides a comprehensive overview of the latest research in the field.
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This edited volume offers a detailed account on the theory of directed graphs from the perspective of important classes of digraphs, with each chapter written by experts on the topic.Outlining fundamental discoveries and new results obtained over recent years, this book provides a comprehensive overview of the latest research in the field.
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A class of upper‐embeddable graphs
Journal of Graph Theory, 1979AbstractIn this paper, we prove the following result: Every graph obtained by connecting (with any number of edges) two vertex‐disjoint upper‐embeddable graphs graphs with even Betti number is upper‐embeddable.
François Jaeger +2 more
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