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Rectification of Circular Arcs by Linkages
The Mathematical Intelligencer, 2019In this paper, the authors give various ways to rectify the arc of a circle, that is, to construct a straight line of the same arc length.
Dawson R., Milici P.
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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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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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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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An approximation method to circular arcs
Applied Mathematics and Computation, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhi Liu 0007 +3 more
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From a Circular-Arc Model to a Proper Circular-Arc Model
2008We are given a circular-arc graph, represented by a circular-arc model; our goal is to decide whether the graph is a proper circular-arc graph. We do so in time linear in the number of vertices of the graph, regardless of the number of edges which may be quadratic in the number of vertices. For every input graph, we either provide a proper circular-arc
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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, 1990The 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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Approximation of Polylines with Circular Arcs
2004Approximation of piecewise linear polylines with circle arcs is an important problem. The approximation is used for polyline compression, noise filtering, feature detection, and inspection of mechanical parts [1-5]. A new accurate and fast iterative method of polyline approximation with a circle arc is described in the paper.
Eugene Bodansky, Alexander Gribov
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Coloring a Family of Circular Arcs
SIAM Journal on Applied Mathematics, 1975This paper presents a collection of results about coloring a family of circular arcs. We prove that the strong perfect graph conjecture is valid for circular-arc graphs. We give some upper bounds on the number of colors needed to color various families of arcs.
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