Edge‐colored complete graphs without properly colored even cycles: A full characterization
The structure of edge‐colored complete graphs containing no properly colored triangles has been characterized by Gallai back in the 1960s. More recently, Cǎda et al. and Fujita et al. independently determined the structure of edge‐colored complete bipartite graphs containing no properly colored C 4....
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| Veröffentlicht in: | Journal of graph theory 2021-09, Vol.98 (1), p.110-124 |
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| container_title | Journal of graph theory |
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| creator | Li, Ruonan Broersma, Hajo Yokota, Maho Yoshimoto, Kiyoshi |
| description | The structure of edge‐colored complete graphs containing no properly colored triangles has been characterized by Gallai back in the 1960s. More recently, Cǎda et al. and Fujita et al. independently determined the structure of edge‐colored complete bipartite graphs containing no properly colored
C
4. We characterize the structure of edge‐colored complete graphs containing no properly colored even cycles, or equivalently, without a properly colored
C
4 or
C
6. In particular, we first deal with the simple case of 2‐edge‐colored complete graphs, using a result of Yeo. Next, for
k
≥
3, we define four classes of
k‐edge‐colored complete graphs without properly colored even cycles and prove that any
k‐edge‐colored complete graph without a properly colored even cycle belongs to one of these four classes. |
| doi_str_mv | 10.1002/jgt.22684 |
| format | Article |
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C
4. We characterize the structure of edge‐colored complete graphs containing no properly colored even cycles, or equivalently, without a properly colored
C
4 or
C
6. In particular, we first deal with the simple case of 2‐edge‐colored complete graphs, using a result of Yeo. Next, for
k
≥
3, we define four classes of
k‐edge‐colored complete graphs without properly colored even cycles and prove that any
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C
4. We characterize the structure of edge‐colored complete graphs containing no properly colored even cycles, or equivalently, without a properly colored
C
4 or
C
6. In particular, we first deal with the simple case of 2‐edge‐colored complete graphs, using a result of Yeo. Next, for
k
≥
3, we define four classes of
k‐edge‐colored complete graphs without properly colored even cycles and prove that any
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C
4. We characterize the structure of edge‐colored complete graphs containing no properly colored even cycles, or equivalently, without a properly colored
C
4 or
C
6. In particular, we first deal with the simple case of 2‐edge‐colored complete graphs, using a result of Yeo. Next, for
k
≥
3, we define four classes of
k‐edge‐colored complete graphs without properly colored even cycles and prove that any
k‐edge‐colored complete graph without a properly colored even cycle belongs to one of these four classes.</abstract><cop>Hoboken</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/jgt.22684</doi><tpages>15</tpages><orcidid>https://orcid.org/0000-0001-5419-1533</orcidid><orcidid>https://orcid.org/0000-0002-4678-3210</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of graph theory, 2021-09, Vol.98 (1), p.110-124 |
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| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | complete graph edge‐colored graph forbidden subgraph Graph coloring Graphs properly colored cycle Structural analysis |
| title | Edge‐colored complete graphs without properly colored even cycles: A full characterization |
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