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Chromatic number of sparse colored mixed planar graphs
Institution:1. Dept. Matemàtica Aplicada IV, UPC, Barcelona, Spain;2. LIRMM, Univ. Montpellier 2, 161 rue Ada, 34392 Montpellier Cedex 5, France;3. LaBRI, Univ. Bordeaux 1, 351 Cours de la Libération, 33405 Talence, France;1. Mathematics Department, Princeton University, Princeton, NJ 08544, USA;2. Department of Applied Mathematics, Computer Science and Statistics, Ghent University, 9000 Ghent, Belgium;3. Computer Science Department, University of Mons, 7000 Mons, Belgium;4. Institut für Informatik, Universität zu Köln, 50931 Köln, Germany;5. Department of Computer Science, Lehman College, CUNY, Bronx, NY 10468, USA;1. Indian Institute of Information Technology Kottayam, India;2. Indian Institute of Information Technology Design and Manufacturing Kancheepuram, Chennai, India
Abstract:A colored mixed graph has vertices linked by both colored arcs and colored edges. The chromatic number of such a graph G is defined as the smallest order of a colored mixed graph H such that there exists a (arc-color preserving) homomorphism from G to H. We study in this paper the colored mixed chromatic number of planar graphs, partial 2-trees and outerplanar graphs with given girth.
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