论文标题
汉密尔顿周期的幂图被随机几何图扰动
Powers of Hamilton cycles in dense graphs perturbed by a random geometric graph
论文作者
论文摘要
令$ g $是作为某些$ n $ vertex图的结合$ h_n $，最低度$δ（h_n）\geqαn$和a $ d $ - 二维随机几何图$ g^d（n，r）$。我们在$ r $的条件下调查图$ g $ will a.a.s.包含汉密尔顿周期的$ k $ th功率，以$ h_n $的任何选择。我们为所有$α$，$ d $和$ k $的$ r $提供渐近最佳条件。这在遏制其他跨越结构（例如$ f $ factors）中具有应用程序。
Let $G$ be a graph obtained as the union of some $n$-vertex graph $H_n$ with minimum degree $δ(H_n)\geqαn$ and a $d$-dimensional random geometric graph $G^d(n,r)$. We investigate under which conditions for $r$ the graph $G$ will a.a.s. contain the $k$-th power of a Hamilton cycle, for any choice of $H_n$. We provide asymptotically optimal conditions for $r$ for all values of $α$, $d$ and $k$. This has applications in the containment of other spanning structures, such as $F$-factors.
