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The Phylogeny Graphs of Doubly Partial Orders
Discussiones Mathematicae Graph Theory, 2013 The competition graph of a doubly partial order is known to be an interval graph. The CCE graph and the niche graph of a doubly partial order are also known to be interval graphs if the graphs do not contain a cycle of length four and three as an induced
Park Boram, Sano Yoshio
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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
Lefteris M. Kirousis +1 more
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A Characterization of 2-Tree Probe Interval Graphs
Discussiones Mathematicae Graph Theory, 2014 A graph is a probe interval graph if its vertices correspond to some set of intervals of the real line and can be partitioned into sets P and N so that vertices are adjacent if and only if their corresponding intervals intersect and at least one belongs ...
Brown David E. +2 more
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Open-interval graphs versus closed-interval graphs
Discrete Mathematics, 1987 It is proved that a countable graph is a closed-interval graph if and only if it is an open-interval graph. A counter-example is given for uncountable graphs. Also the case of unit length intervals is studied.
Peter Frankl, Hiroshi Maehara
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Mathematics, 2019 Fuzzy graphs (FGs) and their generalizations have played an essential role in dealing with real-life problems involving uncertainties. The goal of this article is to show some serious flaws in the existing definitions of several root-level generalized FG
Naeem Jan +6 more
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Large-girth roots of graphs [PDF]
, 2010 We study the problem of recognizing graph powers and computing roots of graphs. Our focus is on classes of graphs with no short cycles. We provide a polynomial time recognition algorithm for r-th powers of graphs of girth at least 2r vertical bar 3, thus
Adamaszek, Michal +4 more
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The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs
Discussiones Mathematicae Graph Theory, 2017 A distinguishing coloring of a graph G is a coloring of the vertices so that every nontrivial automorphism of G maps some vertex to a vertex with a different color. The distinguishing number of G is the minimum k such that G has a distinguishing coloring
Immel Poppy, Wenger Paul S.
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A characterization of the interval function of a (finite or infinite) connected graph [PDF]
, 2001 summary:By the interval function of a finite connected graph we mean the interval function in the sense of H. M. Mulder. This function is very important for studying properties of a finite connected graph which depend on the distance between vertices ...
Nebeský, Ladislav
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On Generalizations of Pairwise Compatibility Graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceA graph $G$ is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree and an interval $I$, such that each leaf of the tree is a vertex of the graph, and there is an edge $\{ x, y \}$ in $G$ if and only if the weight of the path in the
Tiziana Calamoneri +3 more
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