Cycle decompositions and constructive characterizations
Decomposing an Eulerian graph into a minimum respectively maximum number of edge disjoint cycles is an NP-complete problem. We prove that an Eulerian graph decomposes into a unique number of cycles if and only if it does not contain two edge disjoint cycles sharing three or more vertices. To this en...
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| Format: | EJournal Article |
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2019-10-10.
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| LEADER | 02137 am a22002773u 4500 | ||
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| 001 | 0 nhttps:__www.ejgta.org_index.php_ejgta_article_downloadSuppFile_731_110 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Heinrich, Irene; Technische Universität Kaiserslautern |e author |
| 100 | 1 | 0 | |e contributor |
| 700 | 1 | 0 | |a Streicher, Manuel; Technische Universität Kaiserslautern |e author |
| 245 | 0 | 0 | |a Cycle decompositions and constructive characterizations |
| 260 | |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, |c 2019-10-10. | ||
| 500 | |a https://www.ejgta.org/index.php/ejgta/article/view/731 | ||
| 520 | |a Decomposing an Eulerian graph into a minimum respectively maximum number of edge disjoint cycles is an NP-complete problem. We prove that an Eulerian graph decomposes into a unique number of cycles if and only if it does not contain two edge disjoint cycles sharing three or more vertices. To this end, we discuss the interplay of three binary graph operators leading to novel constructive characterizations of two subclasses of Eulerian graphs. This enables us to present a polynomial-time algorithm which decides whether the number of cycles in a cycle decomposition of a given Eulerian graph is unique. | ||
| 540 | |a Copyright (c) 2019 Electronic Journal of Graph Theory and Applications (EJGTA) | ||
| 546 | |a eng | ||
| 690 | |a constructive characterization, cycle decomposition, cycle packing, cycle covering, Eulerian graphs | ||
| 655 | 7 | |a info:eu-repo/semantics/article |2 local | |
| 655 | 7 | |a info:eu-repo/semantics/publishedVersion |2 local | |
| 655 | 7 | |a Peer-reviewed Article |2 local | |
| 786 | 0 | |n Electronic Journal of Graph Theory and Applications (EJGTA); Vol 7, No 2 (2019): Electronic Journal of Graph Theory and Applications; 411 - 428 | |
| 786 | 0 | |n 2338-2287 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/view/731/pdf_120 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/downloadSuppFile/731/110 | |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/view/731/pdf_120 |z Get Fulltext |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/downloadSuppFile/731/110 |z Get Fulltext |