On 1-rotational decompositions of complete graphs into tripartite graphs
Consider a tripartite graph to be any simple graph that admits a proper vertex coloring in at most 3 colors. Let \(G\) be a tripartite graph with \(n\) edges, one of which is a pendent edge. This paper introduces a labeling on such a graph \(G\) used to achieve 1-rotational \(G\)-decompositions of \...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2019-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | https://www.opuscula.agh.edu.pl/vol39/5/art/opuscula_math_3936.pdf |
| _version_ | 1818280270176976896 |
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| author | Ryan C. Bunge |
| author_facet | Ryan C. Bunge |
| author_sort | Ryan C. Bunge |
| collection | DOAJ |
| description | Consider a tripartite graph to be any simple graph that admits a proper vertex coloring in at most 3 colors. Let \(G\) be a tripartite graph with \(n\) edges, one of which is a pendent edge. This paper introduces a labeling on such a graph \(G\) used to achieve 1-rotational \(G\)-decompositions of \(K_{2nt}\) for any positive integer \(t\). It is also shown that if \(G\) with a pendent edge is the result of adding an edge to a path on \(n\) vertices, then \(G\) admits such a labeling. |
| first_indexed | 2024-12-12T23:46:33Z |
| format | Article |
| id | doaj.art-f4f1fe52af1e40eb91027fd49d338114 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-12T23:46:33Z |
| publishDate | 2019-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-f4f1fe52af1e40eb91027fd49d3381142022-12-22T00:06:49ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742019-01-01395623643https://doi.org/10.7494/OpMath.2019.39.5.6233936On 1-rotational decompositions of complete graphs into tripartite graphsRyan C. Bunge0https://orcid.org/0000-0003-0051-379XIllinois State University, Department of Mathematics, Normal, IL 61790-4520, USAConsider a tripartite graph to be any simple graph that admits a proper vertex coloring in at most 3 colors. Let \(G\) be a tripartite graph with \(n\) edges, one of which is a pendent edge. This paper introduces a labeling on such a graph \(G\) used to achieve 1-rotational \(G\)-decompositions of \(K_{2nt}\) for any positive integer \(t\). It is also shown that if \(G\) with a pendent edge is the result of adding an edge to a path on \(n\) vertices, then \(G\) admits such a labeling.https://www.opuscula.agh.edu.pl/vol39/5/art/opuscula_math_3936.pdfgraph decomposition1-rotationalvertex labeling |
| spellingShingle | Ryan C. Bunge On 1-rotational decompositions of complete graphs into tripartite graphs Opuscula Mathematica graph decomposition 1-rotational vertex labeling |
| title | On 1-rotational decompositions of complete graphs into tripartite graphs |
| title_full | On 1-rotational decompositions of complete graphs into tripartite graphs |
| title_fullStr | On 1-rotational decompositions of complete graphs into tripartite graphs |
| title_full_unstemmed | On 1-rotational decompositions of complete graphs into tripartite graphs |
| title_short | On 1-rotational decompositions of complete graphs into tripartite graphs |
| title_sort | on 1 rotational decompositions of complete graphs into tripartite graphs |
| topic | graph decomposition 1-rotational vertex labeling |
| url | https://www.opuscula.agh.edu.pl/vol39/5/art/opuscula_math_3936.pdf |
| work_keys_str_mv | AT ryancbunge on1rotationaldecompositionsofcompletegraphsintotripartitegraphs |