Results 211 to 220 of about 7,309 (246)
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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
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Clique graphs of Helly circular-arc graphs.
Ars Comb., 2001 A graph \(G\) is a Helly circular-arc graph if \(G\) can be represented as the intersection graph of a system of arcs on a circle such that the arcs satisfy the Helly property. The clique graph of \(G\) is the intersection graph of the cliques of \(G\). In the paper, clique graphs of Helly circular-arc graphs are characterized in terms of the existence
Guillermo Durán 0001, Min Chih Lin
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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 the Helly Property then M is a Helly circular-arc model.
Min Chih Lin +2 more
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Minimum Fill-in on Circle and Circular-Arc Graphs [PDF]
Journal of Algorithms, 1996 Summary: 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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Restricted circular-arc graphs and clique cycles
Discrete Mathematics, 2003 Circular-arc graphs are natural analogs of chordal and interval graphs, but without some of the features that make chordal and interval graphs particularly nice; perhaps, the biggest difference is the failure of the Helly condition.
Terry A Mckee
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Treewidth of Circular-Arc Graphs
SIAM Journal on Discrete Mathematics, 1994It is shown that the treewidth of circular-arc graphs and the corresponding tree-decomposition can be found in \(O(n^ 3)\) time. Let \(G= (V,E)\) be a circular-arc graph corresponding to a family \(\{A_ 0, A_ 1,\dots, A_{n-1}\}\) of arcs on a unit circle. Define a left clique \(S_ i\) by \(S_ i= \{A_ j\mid A_ j\) contains the left end points of \(A_ i\}
Ravi Sundaram +2 more
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Characterizations and recognition of circular-arc graphs and subclasses: A survey [PDF]
Discrete Mathematics, 2009 Circular graphs are intersection graphs of arcs on a circle. These graphs are reported to have been studied since 1964, and they have been receiving considerable attention since a series of papers by Tucker in the 1970s.
Min Chih Lin, Jayme L Szwarcfiter
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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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Stability in circular arc graphs
Journal of Algorithms, 1988Summary: An algorithm is presented which finds a maximum stable set of a family of n arcs on a circle in O(n log n) time given the arcs as an unordered list of their endpoints or in O(n) time if they are already sorted. If we are given only the circular arc graph without a circular arc representation for it, then a maximum stable set can be found in ...
Martin Charles Golumbic, Peter L. Hammer
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