IEICE Technical Committee Submission System
Conference Paper's Information
Online Proceedings
[Sign in]
Tech. Rep. Archives
 Go Top Page Go Previous   [Japanese] / [English] 

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
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 COMP2008-11

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  
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.)
3rd Author's Name  
3rd Author's Affiliation ()
4th Author's Name  
4th Author's Affiliation ()
5th Author's Name  
5th Author's Affiliation ()
6th Author's Name  
6th Author's Affiliation ()
7th Author's Name  
7th Author's Affiliation ()
8th Author's Name  
8th Author's Affiliation ()
9th Author's Name  
9th Author's Affiliation ()
10th Author's Name  
10th Author's Affiliation ()
11th Author's Name  
11th Author's Affiliation ()
12th Author's Name  
12th Author's Affiliation ()
13th Author's Name  
13th Author's Affiliation ()
14th Author's Name  
14th Author's Affiliation ()
15th Author's Name  
15th Author's Affiliation ()
16th Author's Name  
16th Author's Affiliation ()
17th Author's Name  
17th Author's Affiliation ()
18th Author's Name  
18th Author's Affiliation ()
19th Author's Name  
19th Author's Affiliation ()
20th Author's Name  
20th Author's Affiliation ()
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 

[Return to Top Page]

[Return to IEICE Web Page]

The Institute of Electronics, Information and Communication Engineers (IEICE), Japan