Proper circular arc graphs as intersection graphs of pathson a grid
نویسندگان
چکیده
منابع مشابه
Proper Helly Circular-Arc Graphs
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. A (proper) (unit) (Helly) circular-arc graph is the intersection graph of the arcs of a (...
متن کاملHadwiger's conjecture for proper circular arc graphs
Circular arc graphs are graphs whose vertices can be represented as arcs on a circle such that any two vertices are adjacent if and only if their corresponding arcs intersect. Proper circular arc graphs are graphs which have a circular arc representation where no arc is completely contained in any other arc. Hadwiger’s conjecture states that if a graph G has chromatic number k, then a complete ...
متن کاملOn the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
Golumbic, Lipshteyn and Stern proved that every graph can be represented as the edge intersection graph of paths on a grid, i.e., one can associate to each vertex of E-mail addresses: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]. This work was partially supported by MathAmSud...
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We give two new algorithms for recognizing proper circulararc graphs and unit circular-arc graphs. The algorithms either provide a model for the input graph, or a certificate that proves that such a model does not exist and can be authenticated in O(n) time.
متن کاملFinding intersection models: From chordal to Helly circular-arc graphs
Every chordal graph G admits a representation as the intersection graph of a family of subtrees of a tree. A classic way of finding such an intersection model is to look for a maximum spanning tree of the valuated clique graph of G. Similar techniques have been applied to find intersection models of chordal graph subclasses as interval graphs and path graphs. In this work, we extend those metho...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2019
ISSN: 0166-218X
DOI: 10.1016/j.dam.2019.02.010