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| 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 |
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| 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. |
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| 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 |
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| 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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