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Please use this identifier to cite or link to this item: http://hdl.handle.net/2005/475

Title: Hadwiger's Conjecture On Circular Arc Graphs
Authors: Belkale, Naveen
Advisors: Chandran, Sunil
Keywords: Graph Theory
Hadwiger's Conjecture
Circular Arc Graphs
Good Path Set
Successor Function
Clique Minor
Graph Minors
Submitted Date: Jul-2007
Series/Report no.: G21484
Abstract: Conjectured in 1943, Hadwiger’s conjecture is one of the most challenging open problems in graph theory. Hadwiger’s conjecture states that if the chromatic number of a graph G is k, then G has a clique minor of size at least k. In this thesis, we give motivation for attempting Hadwiger’s conjecture for circular arc graphs and also prove the 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 a subclass of circular arc graphs that have a circular arc representation where no arc is completely contained in any other arc. It is interesting to study Hadwiger’s conjecture for circular arc graphs as their clique minor cannot exceed beyond a constant factor of its chromatic number as We show in this thesis. Our main contribution is the proof of Hadwiger’s conjecture for proper circular arc graphs. Also, in this thesis we give an analysis and some basic results on Hadwiger’s conjecture for circular arc graphs in general.
URI: http://etd.iisc.ernet.in/handle/2005/475
Appears in Collections:Computer Science and Automation (csa)

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