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Hadwiger's Conjecture and Squares of Chordal Graphs

Chandran, Sunil L and Issac, Davis and Zhou, Sanming (2016) Hadwiger's Conjecture and Squares of Chordal Graphs. In: 22nd International Computing and Combinatorics Conference (COCOON), AUG 02-04, 2016, Ho Chi Minh City, VIETNAM, pp. 417-428.

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Official URL: http://dx.doi.org/10.1007/978-3-319-42634-1_34

Abstract

Hadwiger's conjecture states that for every graph G, chi(G) <= eta(G), where chi(G) is the chromatic number and eta(G) is the size of the largest clique minor in G. In this work, we show that to prove Hadwiger's conjecture in general, it is sufficient to prove Hadwiger's conjecture for the class of graphs F defined as follows: F is the set of all graphs that can be expressed as the square graph of a split graph. Since split graphs are a subclass of chordal graphs, it is interesting to study Hadwiger's Conjecture in the square graphs of subclasses of chordal graphs. Here, we study a simple subclass of chordal graphs, namely 2-trees and prove Hadwiger's Conjecture for the squares of the same. In fact, we show the following stronger result: If G is the square of a 2-tree, then G has a clique minor of size chi(G), where each branch set is a path.

Item Type: Conference Proceedings
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Additional Information: Copy right for this article belongs to the SPRINGER INT PUBLISHING AG, GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND
Department/Centre: Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)
Date Deposited: 20 Jan 2017 04:31
Last Modified: 20 Jan 2017 04:31
URI: http://eprints.iisc.ernet.in/id/eprint/55943

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