Abstract
In this paper 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 G c (resp., digraph D c) not satisfying π, and an edge-recoloring cost matrix R = [r ij ] c ×c where r ij ≥ 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 G c (resp., oriented edges in D c) in order to construct a new c′-edge-colored \(G^{c'}_{new}\) with c′ ≤ c (resp., \(D^{c'}_{new}\)) such that the total edge-recoloring cost is minimized and property π is satisfied. Here, we are especially concerned with properly edge-colored and monochromatic paths, trails and cycles in graphs and digraphs.
This work was partially supported by FAPERJ (Projects E-26/110.552/2010 and E-26/103.054/2011) and CNPq/Brazil.
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Martinhon, C.A., Faria, L. (2013). The Edge-Recoloring Cost of Paths and Cycles in Edge-Colored Graphs and Digraphs. In: Fellows, M., Tan, X., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7924. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38756-2_24
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