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Structural results on circular-arc graphs and circle graphs: A survey and the main open problems [PDF]
Discrete Applied Mathematics, 2014 Artículo de publicación ISICircular-arc graphs are the intersection graphs of open arcs on a circle. Circle graphs are the intersection graphs of chords on a circle.
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Minimum Cuts for Circular-Arc Graphs
SIAM Journal on Computing, 1990Summary: The problem of finding a minimum cut of n arcs on a unit circle is considered. It is shown that this problem can be solved in \(\Theta\) (n log n) time, which is optimal to within a constant factor. If the endpoints of the arcs are sorted, the problem can be solved in linear time.
D. T. Lee +2 more
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Longest Paths in Circular Arc Graphs
Combinatorics, Probability and Computing, 2004It is shown that all maximum length paths of a connected circular arc graph, or a connected interval graph, have non-empty intersection.
Paul N. Balister +3 more
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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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Independent Sets in Circular-Arc Graphs
Journal of Algorithms, 1995Summary: This paper presents a linear time algorithm for the independent set problem on circular-arc graphs, previous algorithms for this problem have assumed that the input is a set of circular-arcs and solve the problem in \(O (n)\) time. However, the fastest known algorithm for constructing the circular-arc representation from a set of adjacency ...
Wen-Lian Hsu, Jeremy P. Spinrad
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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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Balancedness of some subclasses of circular-arc graphs [PDF]
Electronic Notes in Discrete Mathematics, 2010 A graph is balanced if its clique-vertex incidence matrix is balanced, i.e., it does not contain a square submatrix of odd order with exactly two ones per row and per column.
Flavia Bonomo +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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An Efficient Test for Circular-Arc Graphs
SIAM Journal on Computing, 1980An undirected graph G is called a circular-arc graph if there exists a family of arcs on a circle and a 1–1 correspondence between vertices and arcs such that two distinct vertices are adjacent if and only if the corresponding arcs overlap. Such a family is called a circular-arc model for G.
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