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| 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 |
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| 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 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 | COMP2008-11 |
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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 | Author-1 |
| Date Time | 2008-05-13 13:55:00 |
| Presentation Time | 35 minutes |
| Registration for | COMP |
| Paper # | COMP2008-11 |
| Volume (vol) | vol.108 |
| Number (no) | no.29 |
| Page | pp.25-32 |
| #Pages | 8 |
| Date of Issue | 2008-05-06 (COMP) |
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