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Rapid and Intense Declines of Forest Connectivity in the Amazon Arc of Deforestation Over Four Decades. [PDF]
Glob Chang BiolFavretto MA, Hirota M.
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The clique operator on circular-arc graphs [PDF]
Discrete Applied Mathematics, 2010 A circular-arc graph G is the intersection graph of a collection of arcs on the circle and such a collection is called a model of G. Say that the model is proper when no arc of the collection contains another one, it is Helly when the arcs satisfy the ...
Min Chih Lin, Jayme L Szwarcfiter
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Certifying algorithms for recognizing proper circular-arc graphs and unit circular-arc graphs [PDF]
Discrete Applied Mathematics, 2009 We give two new linear-time algorithms, one for recognizing proper circular-arc graphs and the other for recognizing unit circular-arc graphs. Both algorithms provide either a model for the input graph, or a certificate that proves that such a model does
Haim Kaplan, Yahav Nussbaum
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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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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.
Alan Tucker
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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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Clique-Coloring Circular-Arc Graphs
Electronic Notes in Discrete Mathematics, 2009 Abstract A clique-coloring of a graph is a coloring of its vertices such that no maximal clique of size at least two is monochromatic. A circular-arc graph is the intersection graph of a family of arcs in a circle. We show that every circular-arc graph is 3-clique-colorable.
Márcia R. Cerioli +1 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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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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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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