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Paper Abstract and Keywords
Presentation 2007-06-29 14:40
On the complexity of planar n/k-coloring problems
Masakazu Shoji, Akihiro Uejima (Osaka Electro-Communication Univ.) COMP2007-25
Abstract (in Japanese) (See Japanese page) 
(in English) This paper considers the {\it $n/k$-coloring problem} ({\it Circular Coloring}), which is a
subproblem of the $H$-coloring problem, where $H$ is a simple undirected graph and $n, k$
are positive integers with $n/k \geq 2$. It is known that the $H$-coloring problem is
polynomial time solvable if $H$ is bipartite, otherwise it is NP-complete. Thus,
the subproblem (i.e., the $n/k$-coloring problem) has same results. However, the computational
complexities of these problems on planar graphs are still open.
The analysis of the $n/k$-coloring problem for any fixed $n/k$ with $2 < n/k < 4$ is sufficient
to prove that the problem for any fixed $n/k$ is NP-complete on planar graphs, and this paper
presents that the planar $n/k$-problem with $2 < n/k < 3$ is NP-complete.
Keyword (in Japanese) (See Japanese page) 
(in English) $H$-Coloring / $n/k$-Coloring / Circular Coloring / NP-Completeness / Planar Graphs / / /  
Reference Info. IEICE Tech. Rep., vol. 107, no. 127, COMP2007-25, pp. 55-62, June 2007.
Paper # COMP2007-25 
Date of Issue 2007-06-22 (COMP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF COMP2007-25

Conference Information
Committee COMP  
Conference Date 2007-06-29 - 2007-06-29 
Place (in Japanese) (See Japanese page) 
Place (in English) Hokkaido University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2007-06-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) On the complexity of planar n/k-coloring problems 
Sub Title (in English)  
Keyword(1) $H$-Coloring  
Keyword(2) $n/k$-Coloring  
Keyword(3) Circular Coloring  
Keyword(4) NP-Completeness  
Keyword(5) Planar Graphs  
Keyword(6)  
Keyword(7)  
Keyword(8)  
1st Author's Name Masakazu Shoji  
1st Author's Affiliation Osaka Electro-Communication University (Osaka Electro-Communication Univ.)
2nd Author's Name Akihiro Uejima  
2nd Author's Affiliation Osaka Electro-Communication University (Osaka Electro-Communication Univ.)
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Speaker Author-1 
Date Time 2007-06-29 14:40:00 
Presentation Time 25 minutes 
Registration for COMP 
Paper # COMP2007-25 
Volume (vol) vol.107 
Number (no) no.127 
Page pp.55-62 
#Pages 8 
Date of Issue 2007-06-22 (COMP) 

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