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Graphs and Combinatorics

, Volume 32, Issue 2, pp 707–712 | Cite as

Rainbow Spanning Subgraphs of Small Diameter in Edge-Colored Complete Graphs

  • Sogol Jahanbekam
  • Douglas B. WestEmail author
Original Paper
  • 129 Downloads

Abstract

Let s(nt) be the maximum number of colors in an edge-coloring of the complete graph \(K_n\) that has no rainbow spanning subgraph with diameter at most t. We prove \(s(n,t)={\left( {\begin{array}{c}n-2\\ 2\end{array}}\right) }+1\) for \(n,t\ge 3\), while \(s(n,2)={\left( {\begin{array}{c}n-2\\ 2\end{array}}\right) }+\left\lfloor {\frac{n-1}{2}}\right\rfloor \) for \(n\ne 4\) (and \(s(4,2)=2\)).

Keywords

Spanning subgraph Rainbow subgraph Diameter  Anti-Ramsey number 

Mathematics Subject Classification

05C55 05C35 

References

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    Jahanbekam, S., West, D.B.: Anti-Ramsey problems for \(t\) edge-disjoint rainbow spanning subgraphs: cycles, matchings, or trees. J Graph Theory (2014). (accepted) Google Scholar
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    Montágh, B.: Anti-Ramsey numbers of spanning double stars. Acta Univ. Sapientiae Math. 1, 21–34 (2009)MathSciNetzbMATHGoogle Scholar
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    Montellano-Ballesteros, J.J., Neumann-Lara, V.: An anti-Ramsey theorem on cycles. Graphs Combin. 21, 343–354 (2005)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Japan 2015

Authors and Affiliations

  1. 1.Zhejiang Normal UniversityJinhuaChina
  2. 2.University of IllinoisUrbanaUSA

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