Abstract :

In this talk first we explore an extension of the notion of circular coloring form graphs to signed graphs. In particular we present a bipartite analogue of the generalized Mycielski graphs on odd cycles and investigate their circular chromatic number.
To prove the lower bound of 4 we use an elementary notion of the algebraic topology, namely the winding number of a closed curve, thus presenting in an elementary manner a strong connection between the two subjects.