2006/02/24 by Jaroslav Nešetřil, Jaroslav Nesetril, Robert Šámal +3
Computer Science · Engineering · Mathematics · #05C15 #05C25 #05C38 #3D Modeling in Geospatial Applications #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Constraint Satisfaction and Optimization #FOS: Mathematics #math.CO #msc:05C15 #msc:05C25 #msc:05C38
paper · pdf · doi:10.48550/arxiv.math/0602563
31 pages
arxiv created 2006/02/24 · openalex publication_date 2006/02/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Delta(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 homomorphism-incomparable 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 construction of homotens graphs.