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| Presentation | 2007-12-14 16:15 Formulas on the Numbers of Connected Spanning Subgraphs with at Most n+1 Edges in a Complete Graph Kn Peng Cheng (Nagoya Gakuin Univ.), Shigeru Masuyama (Toyahashi Univ. of Tech.)  COMP2007-53 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | Let $N_{i}$ be the number of all connected spanning subgraphs with $i(n-1\leq i\leq m)$ edges in an $n$-vertex $m$-edge undirected graph $G=(V,E)$. Although $N_{n-1}$ is computed in polynomial time by the Matrix-tree theorem, whether $N_{n}$ is efficiently computed for a graph $G$ is an open problem (see e.g., \cite{CC97}). On the other hand, whether $N_{n}^2\geq N_{n-1}N_{n+1}$ for a graph $G$ is also open as a part of log concave conjecture (see e.g., \cite{Colb93,Welsh71}). In this paper, for a complete graph $K_{n}$, we give the formulas for $N_{n}$, $N_{n+1}$, by which $N_{n}$, $N_{n+1}$ are respectively computed in polynomial time on $n$, and, in particular, prove $N_{n}^{2}> N_{n-1}N_{n+1}$ as well. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | complete graph / connected spanning subgraph / log concave sequence / network reliability polynomial / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 107, no. 390, COMP2007-53, pp. 35-42, Dec. 2007. | |
| Paper # | COMP2007-53 | |
| Date of Issue | 2007-12-07 (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 | COMP2007-53 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2007-12-14 - 2007-12-14 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Hiroshima University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2007-12-COMP |
| Language | English (Japanese title is available) |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Formulas on the Numbers of Connected Spanning Subgraphs with at Most n+1 Edges in a Complete Graph Kn |
| Sub Title (in English) | |
| Keyword(1) | complete graph |
| Keyword(2) | connected spanning subgraph |
| Keyword(3) | log concave sequence |
| Keyword(4) | network reliability polynomial |
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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 | Toyahashi University of Technology (Toyahashi Univ. of Tech.) |
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| Speaker | Author-1 |
| Date Time | 2007-12-14 16:15:00 |
| Presentation Time | 35 minutes |
| Registration for | COMP |
| Paper # | COMP2007-53 |
| Volume (vol) | vol.107 |
| Number (no) | no.390 |
| Page | pp.35-42 |
| #Pages | 8 |
| Date of Issue | 2007-12-07 (COMP) |
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