Results 11 to 20 of about 1,554,742 (257)
Balancedness of subclasses of circular-arc graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Graph TheoryInternational audienceA graph is balanced if its clique-vertex incidence matrix contains no square submatrix of odd order with exactly two ones per row and per column.
Safe, Martin D. +11 more
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On cliques of Helly Circular-arc Graphs
Electronic Notes in Discrete Mathematics, 2008 A circular-arc graph is the intersection graph of a set of arcs on the circle. It is a Helly circular-arc graph if it has a Helly model, where every maximal clique is the set of arcs that traverse some clique point on the circle.
Ross M. Mcconnell B +3 more
core +3 more sources
Hadwiger’s conjecture for proper circular arc graphs [PDF]
European Journal of Combinatorics, 2009 Circular arc graphs are graphs whose vertices can be represented as arcs on a circle such that any two vertices are adjacent if and only if their corresponding arcs intersect. Proper circular arc graphs are graphs which have a circular arc representation
Chandran, L. Sunil +3 more
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A Note on Longest Paths in Circular Arc Graphs
Discussiones Mathematicae Graph Theory, 2015 As observed by Rautenbach and Sereni [SIAM J. Discrete Math. 28 (2014) 335-341] there is a gap in the proof of the theorem of Balister et al. [Combin. Probab. Comput.
Joos Felix
doaj +2 more sources
Partial Characterizations of Circular-Arc Graphs
Electronic Notes in Discrete Mathematics, 2008 A circular-arc graph is the intersection graph of a family of arcs on a circle. A characterization by forbidden induced subgraphs for this class of graphs is not known, and in this work we present a partial result in this direction.
G. Durán +3 more
core +7 more sources
Proper Helly circular-arc graphs
, 2007 . A circular-arc model M = (C, A) is a circle C together with a collection A of arcs of C. If no arc is contained in any other then M is a proper circular-arc model, if every arc has the same length then M is a unit circular-arc model and if A satisfies ...
Min Chih Lin +2 more
core +3 more sources
Clique graphs of Helly circular-arc graphs
Ars Comb., 2001 Clique graphs of several classes of graphs have been already characterized. Trees, interval graphs, chordal graphs, block graphs, clique-Helly graphs are some of them. However, no characterization of clique graphs of circular-arc graphs and some of their
Min Chih Lin, Guillermo Durán
core +3 more sources
Circular-arc graphs and the Helly property
CoRRIn this paper we investigate some problems related to the Helly properties of circular-arc graphs, which are defined as intersection graphs of arcs of a fixed circle.
Derbisz, Jan, Krawczyk, Tomasz
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Boxicity of Circular Arc Graphs [PDF]
Graphs and Combinatorics, 2010 A $k$-dimensional box is the cartesian product $R_1 \times R_2 \times ... \times R_k$ where each $R_i$ is a closed interval on the real line. The {\it boxicity} of a graph $G$, denoted as $box(G)$, is the minimum integer $k$ such that $G$ can be represented as the intersection graph of a collection of $k$-dimensional boxes: that is two vertices are ...
Bhowmick, Diptendu, Chandran, Sunil L
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On powers of circular arc graphs
CoRR, 2022 A class of graphs $\mathcal{C}$ is closed under powers if for every graph $G\in\mathcal{C}$ and every $k\in\mathbb{N}$, $G^k\in\mathcal{C}$. Also $\mathcal{C}$ is strongly closed under powers if for every $k\in\mathbb{N}$, if $G^k\in\mathcal{C}$, then $G^{k+1}\in\mathcal{C}$.
Ashok Kumar Das, Indrajit Paul
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