Edge Colorings of K(m,n) with m+n-1 Colors Which Forbid Rainbow Cycles
For positive integers m, n, the greatest number of colors that can appear in an edge coloring of K(m,n) which avoids rainbow cycles is m + n - 1. Here these colorings are constructively characterized. It turns out that these colorings can be encoded by certain vertex labelings of full binary trees w...
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Georgia Southern University
2017-01-01
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| Series: | Theory and Applications of Graphs |
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| Online Access: | https://digitalcommons.georgiasouthern.edu/tag/vol4/iss1/1 |
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doaj-7c062f41cfc84982b3f12715f4e01bcd2020-11-24T22:18:01ZengGeorgia Southern UniversityTheory and Applications of Graphs2470-98592017-01-014110.20429/tag.2017.040101Edge Colorings of K(m,n) with m+n-1 Colors Which Forbid Rainbow CyclesPeter JohnsonClaire ZhangFor positive integers m, n, the greatest number of colors that can appear in an edge coloring of K(m,n) which avoids rainbow cycles is m + n - 1. Here these colorings are constructively characterized. It turns out that these colorings can be encoded by certain vertex labelings of full binary trees with m + n leafs.https://digitalcommons.georgiasouthern.edu/tag/vol4/iss1/1rainbow subgraphsanti-Ramsey problemsfull binary trees |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Peter Johnson Claire Zhang |
| spellingShingle |
Peter Johnson Claire Zhang Edge Colorings of K(m,n) with m+n-1 Colors Which Forbid Rainbow Cycles Theory and Applications of Graphs rainbow subgraphs anti-Ramsey problems full binary trees |
| author_facet |
Peter Johnson Claire Zhang |
| author_sort |
Peter Johnson |
| title |
Edge Colorings of K(m,n) with m+n-1 Colors Which Forbid Rainbow Cycles |
| title_short |
Edge Colorings of K(m,n) with m+n-1 Colors Which Forbid Rainbow Cycles |
| title_full |
Edge Colorings of K(m,n) with m+n-1 Colors Which Forbid Rainbow Cycles |
| title_fullStr |
Edge Colorings of K(m,n) with m+n-1 Colors Which Forbid Rainbow Cycles |
| title_full_unstemmed |
Edge Colorings of K(m,n) with m+n-1 Colors Which Forbid Rainbow Cycles |
| title_sort |
edge colorings of k(m,n) with m+n-1 colors which forbid rainbow cycles |
| publisher |
Georgia Southern University |
| series |
Theory and Applications of Graphs |
| issn |
2470-9859 |
| publishDate |
2017-01-01 |
| description |
For positive integers m, n, the greatest number of colors that can appear in an edge coloring of K(m,n) which avoids rainbow cycles is m + n - 1. Here these colorings are constructively characterized. It turns out that these colorings can be encoded by certain vertex labelings of full binary trees with m + n leafs. |
| topic |
rainbow subgraphs anti-Ramsey problems full binary trees |
| url |
https://digitalcommons.georgiasouthern.edu/tag/vol4/iss1/1 |
| work_keys_str_mv |
AT peterjohnson edgecoloringsofkmnwithmn1colorswhichforbidrainbowcycles AT clairezhang edgecoloringsofkmnwithmn1colorswhichforbidrainbowcycles |
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