On tension-continuous mappings

Tension-continuous (shortly TT) mappings are mappings between the edge sets of graphs. They generalize graph homomorphisms. From another perspective, tension-continuous mappings are dual to the notion of flow-continuous mappings and the context of nowhere-zero flows motivates several questions considered in this paper. Extending our earlier research we define new constructions and operations for graphs (such as graphs M (G)) and give evidence for the complex relationship of homomorphisms and TT mappings. Particularly, solving an open problem, we display pairs of TT-comparable and homomorphismincomparable graphs with arbitrarily high connectivity. We give a new (and more direct) proof of density of TT order and study graphs such that TT mappings and homomorphisms from them coincide; we call such graphs homotens. We show that most graphs are homotens, on the other hand every vertex of a nontrivial homotens graph is contained in a triangle. This provides a justification for our construct...

• Type: Journal
• Year: 2008
• Where: EJC
• Authors: Jaroslav Nesetril, Robert Sámal
• Keywords: EJC 2007, EJC 2008, Information Technology, Mappings, Tension-continuous Mappings, TT Mappings