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Abstract
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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.
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