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 Author, Editor
 Author(s): Arumugam, S. Chandrasekar, K. Raja Misra, Neeldhara Philip, Geevarghese Saurabh, Saket dblp dblp dblp dblp dblp Not MPG Author(s): Arumugam, S. Chandrasekar, K. Raja Misra, Neeldhara Saurabh, Saket
 Editor(s): Iliopoulos, Costas S. Smyth, William F. dblp dblp Not MPII Editor(s): Iliopoulos, Costas S. Smyth, William F.
 BibTeX cite key*: arumugamchandrasekarmisraphilipsaurabh2011

 Title, Booktitle
 Title*: Algorithmic Aspects of Dominator Colorings in Graphs DomChrom.pdf (477.95 KB) Booktitle*: Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Victoria, BC, Canada, July 20-22, 2011, Revised Selected Papers

 Event, URLs
 URL of the conference: http://webhome.cs.uvic.ca/~wendym/IWOCA/IWOCA_2011.html URL for downloading the paper: http://www.springerlink.com/content/77u164v1175x8485/fulltext.pdf Event Address*: Victoria, Canada Language: English Event Date* (no longer used): Organization: Event Start Date: 20 June 2011 Event End Date: 22 June 2011

 Publisher
 Name*: Springer URL: http://www.springer.com Address*: Berlin Type: Revised Selected Paper

 Vol, No, Year, pp.
 Series: Lecture Notes in Computer Science
 Volume: 7056 Number: Month: Pages: 19-30 Year*: 2011 VG Wort Pages: ISBN/ISSN: 978-3-642-25010-1 Sequence Number: DOI: 10.1007/978-3-642-25011-8

 (LaTeX) Abstract: In this paper we initiate a systematic study of a problem that has the flavor of two classical problems, namely {\sc Coloring} and {\sc Domination}, from the perspective of algorithms and complexity. A {\it dominator coloring} of a graph $G$ is an assignment of colors to the vertices of $G$ such that it is a proper coloring and every vertex dominates all the vertices of at least one color class. The minimum number of colors required for a dominator coloring of $G$ is called the {\it dominator chromatic number} of $G$ and is denoted by $\chi_d(G).$ In the {\sc Dominator Coloring (DC)} problem, a graph $G$ and a positive integer $k$ are given as input and the objective is to check whether $\chi_d(G)\leq k$. We first show that unless P=NP, DC cannot be solved in polynomial time on bipartite, planar, or split graphs. This resolves an open problem posed by Chellali and Maffray [{\it Dominator Colorings in Some Classes of Graphs, Graphs and Combinatorics, 2011}] about the polynomial time solvability of DC on chordal graphs. We then complement these hardness results by showing that the problem is fixed parameter tractable (FPT) on chordal graphs and in graphs which exclude a fixed apex graph as a minor. URL for the Abstract: http://www.springerlink.com/content/77u164v1175x8485/ Keywords: Dominator Coloring, Fixed-Parameter Tractability, Chordal Graphs, Apex-Minor-Free Graphs Copyright Message: Copyright Springer Berlin 2011. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, speciﬁcally the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microﬁlms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Published in the Proceedings of IWOCA 2011, Victoria, Canada, July 20-22, 2011. Lecture Notes in Computer Science, Volume 7056. The original publication is available at www.springerlink.com : http://www.springerlink.com/content/77u164v1175x8485/ Download Access Level: Public

 Correlation
 MPG Unit: Max-Planck-Institut für Informatik MPG Subunit: Algorithms and Complexity Group Audience: popular Appearance: MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort

BibTeX Entry:

@INPROCEEDINGS{arumugamchandrasekarmisraphilipsaurabh2011,
AUTHOR = {Arumugam, S. and Chandrasekar, K. Raja and Misra, Neeldhara and Philip, Geevarghese and Saurabh, Saket},
EDITOR = {Iliopoulos, Costas S. and Smyth, William F.},
TITLE = {Algorithmic Aspects of Dominator Colorings in Graphs},
BOOKTITLE = {Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Victoria, BC, Canada, July 20-22, 2011, Revised Selected Papers},
PUBLISHER = {Springer},
YEAR = {2011},
TYPE = {Revised Selected Paper},
VOLUME = {7056},
PAGES = {19--30},
SERIES = {Lecture Notes in Computer Science},