Geodesic
The maximum number of copies of \(K_{r,s}\) in graphs without long cycles or paths
Changhong Lu1 ; Long-Tu Yuan1 ; Ping Zhang1
1East China Normal University
The electronic journal of combinatorics, Tome 28 (2021) no. 4
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The circumference of a graph is the length of a longest cycle of it. We determine the maximum number of copies of $K_{r,s}$, the complete bipartite graph with classes sizes $r$ and $s$, in 2-connected graphs with circumference less than $k$. As corollaries of our main result, we determine the maximum number of copies of $K_{r,s}$ in $n$-vertex $P_{k}$-free and $M_k$-free graphs for all values of $n$, where $P_k$ is a path on $k$ vertices and $M_k$ is a matching on $k$ edges.
DOI : 10.37236/10178
Classification : 05C35, 05C30, 05C38, 05C12
Mots-clés : complete bipartite graph, generalized Turán number

Changhong Lu  1   ; Long-Tu Yuan  1   ; Ping Zhang  1

1 East China Normal University 
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     author = {Changhong  Lu and Long-Tu Yuan and Ping Zhang},
     title = {The maximum number of copies of {\(K_{r,s}\)} in graphs without long cycles or paths},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {4},
     doi = {10.37236/10178},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/10178/}
}
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Changhong  Lu; Long-Tu Yuan; Ping Zhang. The maximum number of copies of \(K_{r,s}\) in graphs without long cycles or paths. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/10178

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