Showing papers by "Andrey A. Dobrynin published in 2012"
TL;DR: This work presents fourteen new 4-chromatic graphs generated by circles in the plane, which are the first examples of graphs of this kind known to be presented.
Abstract: Let G be a simple 4-regular plane graph and let S be a decomposition of G into edge-disjoint cycles. Suppose that every two adjacent edges on a face belong to different cycles of S. Such a graph G arises as a superposition of simple closed curves in the plane with tangencies disallowed. Studies of coloring of graphs of this kind were originated by Grötzsch. Two 4-chromatic graphs generated by circles in the plane were constructed by Koester in 1984 [10, 11, 12]. Until now, no other examples of such graphs were known. We present fourteen new 4-chromatic graphs generated by circles in the plane.