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Discrete Mathematics, 1985 The interval thickness of a graph G is the minimum clique number of all the interval supergraphs of G. The clique number of a graph is the number of nodes of its biggest complete subgraph. On the other hand, the node- search number is the least number of searchers (pebbles) required to clear the ''contaminated'' edges of a graph. A contaminated edge is
Kirousis, Lefteris M. +1 more
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On the Representation of a PI-Graph
Trends in Computational and Applied Mathematics, 2007 Consider two parallel lines (denoted r1 and r2). A graph is a PI graph (Point-Interval graph) if it is an intersection graph of a family F of triangles between r1 and r2 such that each triangle has an interval with two endpoints on r1 and a vertex (a ...
S.M. Almeida, C.P. de Mello, A. Gomide
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Reconstruction of interval graphs
Theoretical Computer Science, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kiyomi, Masashi +2 more
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Betweenness in graphs: A short survey on shortest and induced path betweenness
AKCE International Journal of Graphs and Combinatorics, 2019 Betweenness is a universal notion present in several disciplines of mathematics. The notion of betweenness has a profound history and many pioneers like Euclid, Pasch, Hilbert have studied betweenness axiomatically.
Manoj Changat +2 more
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Interval-valued bipolar fuzzy line graphs
BMC Research Notes, 2023 Objectives The notion of Bipolarity based on positive and negative outcomes. It is well known that bipolar models give more precision, flexibility, and compatibility to the system as compared to the classical models and fuzzy models.
Keneni Abera Tola +2 more
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Cliques and Clique Covers in Interval-Valued Fuzzy Graphs
International Journal of Computational Intelligence Systems, 2021 Finding cliques and clique covers in graphs are one of the most needful tasks. In this paper, interval-valued fuzzy cliques (IVFQs) and interval-valued fuzzy clique covers (IVFQCs) of an interval-valued fuzzy graph (IVFG) are introduced by introducing ...
Napur Patra +3 more
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Polynomial kernels for Proper Interval Completion and related problems
, 2011 Given a graph G = (V,E) and a positive integer k, the Proper Interval Completion problem asks whether there exists a set F of at most k pairs of (V \times V)\E such that the graph H = (V,E \cup F) is a proper interval graph.
Bessy, Stéphane, Perez, Anthony
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The LexCycle on $\overline{P_{2}\cup P_{3}}$-free Cocomparability Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A graph $G$ is a cocomparability graph if there exists an acyclic transitive orientation of the edges of its complement graph $\overline{G}$. LBFS$^{+}$ is a variant of the generic Lexicographic Breadth First Search (LBFS), which uses a specific tie ...
Xiao-Lu Gao, Shou-Jun Xu
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Recognizing edge clique graphs among interval graphs and probe interval graphs
Applied Mathematics Letters, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kong, Jing, Wu, Yaokun
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Coloring problem of signed interval graphs [PDF]
Transactions on Combinatorics, 2019 A signed graph $(G,\sigma)$ is a graph together with an assignment of signs $\{+,-\}$ to its edges where $\sigma$ is the subset of its negative edges.
Farzaneh Ramezani
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