The edge-recoloring cost of monochromatic and properly edge-colored paths and cycles

Faria Luerbio (1) , Laurent Gourvès (2) , Carlos A. Martinhon (3) , Jérôme Monnot (2)

1 UERJ - Universidade do Estado do Rio de Janeiro [Brasil] = Rio de Janeiro State University [Brazil] = Université d'État de Rio de Janeiro [Brésil]
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
3 Department of Computer Science [Beer-Sheva]

We introduce a number of problems regarding edge-color modifications in edge-colored graphs and digraphs. Consider a property π, a c -edge-colored graph GcGc not satisfying π, and an edge-recoloring cost matrix R=[rij]c×cR=[rij]c×c where rij≥0rij≥0 denotes the cost of changing color i of edge e to color j. Basically, in this kind of problem the idea is to change the colors of one or more edges of GcGc in order to construct a new edge-colored graph such that the total edge-recoloring cost is minimized and property π is satisfied. We also consider the destruction of potentially undesirable structures with the minimum edge-recoloring cost. In this paper, we are especially concerned with the construction and destruction of properly edge-colored and monochromatic paths, trails and cycles in graphs and digraphs. Some related problems and future directions are presented.

Mots clés: Edge-colored graphs; Properly edge-colored paths; Trails and cycles; Monochromatic paths; Edge-recoloring cost

Domaines: Informatique [cs]

Faria Luerbio, Laurent Gourvès, Carlos A. Martinhon, Jérôme Monnot. The edge-recoloring cost of monochromatic and properly edge-colored paths and cycles. Theoretical Computer Science, 2015, 602, ⟨10.1016/j.tcs.2015.08.016⟩. ⟨hal-01426672⟩