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


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 \(s(4,2)=2\)).


Spanning subgraph Rainbow subgraph Diameter  Anti-Ramsey number 

Mathematics Subject Classification

05C55 05C35 


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Copyright information

© Springer Japan 2015

Authors and Affiliations

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

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