On λ-fold Rosa-type Labelings of Bipartite Multigraphs
© 2017 Elsevier B.V. It is known that for a given (simple) graph G with n edges, there exits a cyclic G-decomposition of K 2n+1 if and only if G admits a ρ-labeling. It is also known that if G is bipartite and it admits an ordered ρ-labeling, then there exists a cyclic G-decomposition of K 2nx+1 f...
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| Main Authors: | , , , , |
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| Format: | Journal |
| Published: |
2017
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| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85021397534&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/40317 |
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| Institution: | Chiang Mai University |
| Summary: | © 2017 Elsevier B.V. It is known that for a given (simple) graph G with n edges, there exits a cyclic G-decomposition of K 2n+1 if and only if G admits a ρ-labeling. It is also known that if G is bipartite and it admits an ordered ρ-labeling, then there exists a cyclic G-decomposition of K 2nx+1 for every positive integer x. We extend these concepts to labelings of multigraphs through what we call λ-fold ρ-labelings and ordered λ-fold ρ-labelings. Let Kmλ denote the λ-fold complete graph of order m. We sho that if a subgraph G of K2n/λ+1λ has size n, there exits a cyclic G-decomposition of K2n/λ+1λ if and only if G admits a λ-fold ρ-labeling. If in addition G is bipartite and it admits an ordered λ-fold ρ-labeling, then there exists a cyclic G-decomposition of K2nx/λ+1λ for every positive integer x. We discuss some classes of graphs and multigraphs that admit such labelings. |
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