scholarly journals On the upper bound of the diameter of interchange graphs

1999 ◽  
Vol 195 (1-3) ◽  
pp. 277-285 ◽  
Author(s):  
Jianguo Qian
Keyword(s):  
Upper Bound ◽  
Interchange Graphs

scholarly journals A Note on the Number of Edges Guaranteeing a $C_4$ in Eulerian Bipartite Digraphs

10.37236/1667 ◽  
2002 ◽  
Vol 9 (1) ◽  
Author(s):  
Jian Shen ◽  
Raphael Yuster
Keyword(s):  
Upper Bound ◽  
Directed Cycle ◽  
Type Result ◽  
Vertex Partition ◽  
Bipartite Digraph ◽  
Interchange Graphs

Let $G$ be an Eulerian bipartite digraph with vertex partition sizes $m,n$. We prove the following Turán-type result: If $e(G) > 2mn/3$ then $G$ contains a directed cycle of length at most 4. The result is sharp. We also show that if $e(G)=2mn/3$ and no directed cycle of length at most 4 exists, then $G$ must be biregular. We apply this result in order to obtain an improved upper bound for the diameter of interchange graphs.

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