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Algorithms on circular‐arc graphs
Networks, 1974AbstractConsider a finite family of non‐empty sets. The intersection graph of this family is obtained by representing each set by a vertex, two vertices being connected by an edge if and only if the corresponding sets intersect. The intersection graph of a family of arcs on a circularly ordered set is called a circular‐arc graph.
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Parallel algorithms on circular-arc graphs
Information Processing Letters, 1990zbMATH Open Web Interface contents unavailable due to conflicting licenses.
BERTOSSI A. A, MORETTI, SABRINA
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List Homomorphisms and Circular Arc Graphs
Combinatorica, 1999The list homomorphism problem for a graph \(H\) has as input a graph \(G\) and lists \(L(v)\subseteq V(H)\) for the vertices \(v\in V(G)\). The output is a homomorphism \(f:G\to H\) with \(f(v)\in L(v)\) for every \(v\in V(G)\). It is shown that if \(H\) is loopless then this problem is polynomially solvable if \(\overline{H}\) is a circular arc graph ...
Tomás Feder +2 more
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Interval bigraphs and circular arc graphs
Journal of Graph Theory, 2004AbstractWe prove that the complements of interval bigraphs are precisely those circular arc graphs of clique covering number two, which admit a representation without two arcs covering the whole circle. We give another characterization of interval bigraphs, in terms of a vertex ordering, that we hope may prove helpful in finding a more efficient ...
Pavol Hell, Jing Huang 0007
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Polynomial time recognition of unit circular-arc graphs [PDF]
Journal of Algorithms, 2006 We present an efficient algorithm for recognizing unit circular-arc (UCA) graphs, based on a characterization theorem for UCA graphs proved by Tucker in the seventies. Given a proper circular-arc (PCA) graph G, the algorithm starts from a PCA model for G,
Guillermo Duran +2 more
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Two remarks on circular arc graphs
Graphs and Combinatorics, 1997A graph \(G\) is said to be a circular arc graph if there exist circular arcs A\(g\), \(g\in V(G)\), such that \(g\), \(g'\) are adjacent in \(G\) if and only if the corresponding A\(g\), A\(_{g'}\) intersect. This paper shows that a graph with clique covering number two is a circular arc graph if and only if its edges can be coloured by two colours so
Pavol Hell, Jing Huang 0007
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Efficient algorithms for interval graphs and circular‐arc graphs
Networks, 1982AbstractWe show that for an interval graph given in the form of a family of intervals, a maximum independent set, a minimum covering by disjoint completely connected sets or cliques, and a maximum clique can all be found in O(n log n) time [O(n) time if the endpoints of the intervals are sorted].
Udaiprakash I. Gupta +2 more
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k Best Cuts for Circular-Arc graphs
Algorithmica, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kuo-Hui Tsai, D. T. Lee
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Minimum Fill-in on Circle and Circular-Arc Graphs
Journal of Algorithms, 1996Summary: We described elegant and efficient algorithms for solving the MINIMUM FILL-IN problem on circle graphs and circular-arc graphs, which are based on representation theorems for the minimal triangulations of such graphs. Representation theorems of this type are powerful tools for designing treewidth and minimum fill-in algorithms.
Kloks, T., Kratsch, D., Wong, C.K.
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NC algorithms for circular-arc graphs
1989Circular-arc graphs are an important class of intersection graphs. They have been applied to problems in genetics [17], traffic control [18], multidimensional scaling [11], computer compiler design [22], characterization of a certain class of lattices [19], and some other areas [13] [23].
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