论文标题
在外平面图中，反碰撞数量的匹配数提高了界限
Improved bounds for anti-Ramsey numbers of matchings in outerplanar graphs
论文作者
论文摘要
令$ \ mathcal {o} _n $为订单$ n $的所有最大外平面图的集合。令$ ar（\ Mathcal {o} _n，f）$表示最大正整数$ k $，这样$ t \ in \ nathcal {o} _n $没有$ k $ ed $ t $ $ t $的$ k $ f $。用$ m_k $表示大小$ k $的匹配。在本文中，我们证明了$ ar（\ Mathcal {o} _n，m_k）\ le n+4k-9 $对于$ n \ ge3k-3 $，它表达改善了$ ar的现有上限（\ mathcal {o} _n，m_k）$。我们还证明了$ ar（\ Mathcal {o} _n，m_5）= n+4 $ for All $ n \ ge 15 $。
Let $\mathcal{O}_n$ be the set of all maximal outerplanar graphs of order $n$. Let $ar(\mathcal{O}_n,F)$ denote the maximum positive integer $k$ such that $T\in \mathcal{O}_n$ has no rainbow subgraph $F$ under a $k$-edge-coloring of $T$. Denote by $M_k$ a matching of size $k$. In this paper, we prove that $ar(\mathcal{O}_n,M_k)\le n+4k-9$ for $n\ge3k-3$, which expressively improves the existing upper bound for $ar(\mathcal{O}_n,M_k)$. We also prove that $ar(\mathcal{O}_n,M_5)=n+4$ for all $n\ge 15$.
