Results 191 to 200 of about 4,192 (230)

An Efficient Test for Circular-Arc Graphs

SIAM Journal on Computing, 1980
An 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.
Alan Tucker
exaly   +3 more sources

Treewidth of Circular-Arc Graphs

SIAM Journal on Discrete Mathematics, 1994
It 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
openaire   +2 more sources

Stability in circular arc graphs

Journal of Algorithms, 1988
Summary: 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
openaire   +2 more sources

Longest Paths in Circular Arc Graphs

Combinatorics, Probability and Computing, 2004
It 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
openaire   +1 more source

Minimum Cuts for Circular-Arc Graphs

SIAM Journal on Computing, 1990
Summary: 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
openaire   +2 more sources

Algorithms on circular‐arc graphs

Networks, 1974
AbstractConsider 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.
openaire   +2 more sources

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