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| Presentation | 2008-09-11 09:30 Counting Connected Spanning Subgraphs with at Most p+q+1 Edges in a Complete Bipartite Graph Kp,q Peng Cheng (Nagoya Gakuin Univ.), Shigeru Masuyama (Toyohashi Univ. of Technology)  COMP2008-24 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | Let $N_{i}(G)$ denote the number of connected spanning $i$-edge subgraphs in an $n$-vertex $m$-edge undirected graph $G=(V,E)$. Although $N_{n-1}(G)$ is computed in polynomial time by the Matrix-Tree theorem, whether $N_{n}(G)$ is efficiently computed is unknown (see e.g., \cite{CC97}). On the other hand, whether $N_{n}(G)^2\geq N_{n-1}(G)N_{n+1}(G)$ is still open as a part of log concave conjecture (see e.g., \cite{Colb93,Welsh71}). In this paper, for a complete bipartite graph $K_{p,q}$, we explore formulas on $N_{n}(K_{p,q})$, $N_{n+1}(K_{p,q})$ and prove the inequality $\frac{N_{n}(K_{p,q})^{2}}{N_{n-1}(K_{p,q})N_{n+1}(K_{p,q})}>\frac{(p-1)(q-1)}{(p-1)(q-1)-1}$. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | graph formula / complete bipartite graph / connected spanning subgraph / log concave sequence / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 108, no. 206, COMP2008-24, pp. 9-16, Sept. 2008. | |
| Paper # | COMP2008-24 | |
| Date of Issue | 2008-09-04 (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 | COMP2008-24 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2008-09-11 - 2008-09-11 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Nagoya Inst. of Tech. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2008-09-COMP |
| Language | English (Japanese title is available) |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Counting Connected Spanning Subgraphs with at Most p+q+1 Edges in a Complete Bipartite Graph Kp,q |
| Sub Title (in English) | |
| Keyword(1) | graph formula |
| Keyword(2) | complete bipartite graph |
| Keyword(3) | connected spanning subgraph |
| Keyword(4) | log concave sequence |
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| 1st Author's Name | Peng Cheng |
| 1st Author's Affiliation | Nagoya Gakuin University (Nagoya Gakuin Univ.) |
| 2nd Author's Name | Shigeru Masuyama |
| 2nd Author's Affiliation | Toyohashi University of Technology (Toyohashi Univ. of Technology) |
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| Speaker | Author-1 |
| Date Time | 2008-09-11 09:30:00 |
| Presentation Time | 30 minutes |
| Registration for | COMP |
| Paper # | COMP2008-24 |
| Volume (vol) | vol.108 |
| Number (no) | no.206 |
| Page | pp.9-16 |
| #Pages | 8 |
| Date of Issue | 2008-09-04 (COMP) |
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