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Paper Abstract and Keywords
Presentation 2008-05-13 13:55
NP-Completeness of Planar n/k-Coloring Problems for n/k Between 3 and 4
Masakazu Shoji, Akihiro Uejima (Osaka Electro-Communication Univ.) COMP2008-11
Abstract (in Japanese) (See Japanese page) 
(in English) This report considers the $n/k$-coloring problem, which is a subproblem for the $H$-coloring problem, where $H$ is a simple undirected graph and $n$, $k$ are positive integers with $n/k \ge 2$. The computational complexities of $n/k$-coloring problems on general graphs can be obtained directly from the prevoius results concerning $H$-coloring problems. However, the complexities of the problems on \textit{planar graphs} are still open. The analysis for any fixed $n/k$ with $2 < n/k < 3$ or $3 < n/k < 4$ is sufficient to prove that the problems on planar graphs are NP-complete, and NP-completeness of the problems with $2 < n/k < 3$ has been shown in our previous works. This report proves that the problems with $3 < n/k < 4$ are NP-complete.
Keyword (in Japanese) (See Japanese page) 
(in English) $H$-coloring / $n/k$-coloring / NP-complete / planar graph / / / /  
Reference Info. IEICE Tech. Rep., vol. 108, no. 29, COMP2008-11, pp. 25-32, May 2008.
Paper # COMP2008-11 
Date of Issue 2008-05-06 (COMP) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
Copyright
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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)
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Conference Information
Committee COMP  
Conference Date 2008-05-13 - 2008-05-13 
Place (in Japanese) (See Japanese page) 
Place (in English) Kyushu Sangyo University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2008-05-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) NP-Completeness of Planar n/k-Coloring Problems for n/k Between 3 and 4 
Sub Title (in English)  
Keyword(1) $H$-coloring  
Keyword(2) $n/k$-coloring  
Keyword(3) NP-complete  
Keyword(4) planar graph  
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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
Date Time 2008-05-13 13:55:00 
Presentation Time 35 
Registration for COMP 
Paper # IEICE-COMP2008-11 
Volume (vol) IEICE-108 
Number (no) no.29 
Page pp.25-32 
#Pages IEICE-8 
Date of Issue IEICE-COMP-2008-05-06 


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