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Domain Algorithmics-Graphs-Combinatorics
Domain - extra
Year 2014
Starting September 2014
Status Open
Subject Homomorphisms and partitions of signed digraphs
Thesis advisor MANOUSSAKIS Yannis
Co-advisors Reza Naserasr
Laboratory LRI GALaC
Abstract Homomorphism of graphs is a way of generalizing graph coloring results of algebraic flavor. When mixed with a geometric restriction, such graphs embeddable on a surface or more generally a minor closed family, we have some of most challenging problems in graph theory, such as the four color theorem and the Hadwiger's conjecture. The main difficulty here is that the relation between minor and homomorphism is non intuitive.

To address this issue, theory of signed graphs is used. Nottion of minor is extended for signed graphs and certain coloring results are obtained on classes of (signed) graphs satisfying certain minor properties. We have therefore recently started studying the theory of homomorphisms for signed graphs. Thus many of coloring and homomorphism results can be substaintially stengthened and therefore we have a rich and promising subject of study.

We would also consider the extention to signed digraphs, a notion which is not studied much yet and is promising.

Work program We will do a mix of learning and research. We will spend some time on theaching the student the notion of homomorphism and minor for signed graphs. Then after having several research problems in mind we will read more on the problem to learn and do research at the same time.
Extra information
Prerequisite Some graduate cours in graph and main mathematical course in particular linear algebra.
Expected funding Institutional funding
Status of funding Expected
Candidates Maria Abi Aad
user reza.naserasr
Created Saturday 07 of June, 2014 16:03:16 CEST
LastModif Saturday 07 of June, 2014 17:14:52 CEST
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