Paper Abstract and Keywords |
Presentation |
2013-03-18 14:10
A note on lower bounds of the girth of planar C_7-colorable graphs Tatsuo Asano, Akihiro Uejima (Osaka Electro-Comm. Univ.) COMP2012-57 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
This report considers the $C_{2k+1}$-coloring problem, which is a subproblem for the $n/k$-coloring problem,
where $n, k$ are positive integers with $n/k \geq 2$. It has already shown that every planar graph with girth
at least $(20k-2)/3$ has a $C_{2k+1}$-coloring, and the bound for $C_5$-colorability was improved.
In this report, we prove that every triangle-free graph whose all subgraphs have average degree less than
$\frac{20}{9}$ is $C_7$-colorable. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
$n/k$-Coloring / $C_7$-Coloring / Circular Coloring / Planar Graphs / Girths / / / |
Reference Info. |
IEICE Tech. Rep., vol. 112, no. 498, COMP2012-57, pp. 31-38, March 2013. |
Paper # |
COMP2012-57 |
Date of Issue |
2013-03-11 (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) |
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COMP2012-57 |
Conference Information |
Committee |
COMP |
Conference Date |
2013-03-18 - 2013-03-18 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Gifu University |
Topics (in Japanese) |
(See Japanese page) |
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Paper Information |
Registration To |
COMP |
Conference Code |
2013-03-COMP |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
A note on lower bounds of the girth of planar C_7-colorable graphs |
Sub Title (in English) |
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Keyword(1) |
$n/k$-Coloring |
Keyword(2) |
$C_7$-Coloring |
Keyword(3) |
Circular Coloring |
Keyword(4) |
Planar Graphs |
Keyword(5) |
Girths |
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Keyword(7) |
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1st Author's Name |
Tatsuo Asano |
1st Author's Affiliation |
Osaka Electro-Communication University (Osaka Electro-Comm. Univ.) |
2nd Author's Name |
Akihiro Uejima |
2nd Author's Affiliation |
Osaka Electro-Communication University (Osaka Electro-Comm. Univ.) |
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Speaker |
Author-1 |
Date Time |
2013-03-18 14:10:00 |
Presentation Time |
25 minutes |
Registration for |
COMP |
Paper # |
COMP2012-57 |
Volume (vol) |
vol.112 |
Number (no) |
no.498 |
Page |
pp.31-38 |
#Pages |
8 |
Date of Issue |
2013-03-11 (COMP) |
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