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arXiv · 1702.03060

A Variation of the Erd\H{o}s-S\'os Conjecture in Bipartite Graphs

Long-Tu Yuan·Xiao-Dong Zhang
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Abstract

The Erd\H{o}s-S\'{o}s Conjecture states that every graph with average degree more than $k-2$ contains all trees of order $k$ as subgraphs. In this paper, we consider a variation of the above conjecture: studying the maximum size of an $(n,m)$-bipartite graph which does not contain all $(k,l)$-bipartite trees for given integers $n\ge m$ and $k\ge l$. In particular, we determine that the maximum size of an $(n,m)$-bipartite graph which does not contain all $(n,m)$-bipartite trees as subgraphs (or all $(k,2)$-bipartite trees as subgraphs, respectively). Furthermore, all these extremal graphs are characterized.

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Long-Tu Yuan, Xiao-Dong Zhang. 2017-02-10. A Variation of the Erd\H{o}s-S\'os Conjecture in Bipartite Graphs. https://arxiv.org/abs/1702.03060

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