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.
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.
Some graduate cours in graph and main mathematical course in particular linear algebra.
Status of funding
Maria Abi Aad
Samedi 07 juin 2014 16:03:16 CEST
Samedi 07 juin 2014 17:14:52 CEST
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Ecole Doctorale Informatique Paris-Sud
Nicole Bidoit Assistante
Stéphanie Druetta Conseiller aux thèses
ED 427 - Université Paris-Sud
UFR Sciences Orsay
Bat 650 - aile nord - 417
Tel : 01 69 15 63 19
Fax : 01 69 15 63 87
courriel: ed-info à lri.fr