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GRAPH LIMITS AND EXCHANGEABLE RANDOM GRAPHS
A SEQUENTIAL IMPORTANCE SAMPLING ALGORITHM FOR GENERATING RANDOM GRAPHS WITH PRESCRIBED DEGREES。
For a graph $G$, denote by $t(G)$ (resp. $b(G)$) the maximum size of a triangle-free (resp. bipartite) subgraph of $G$. Of course $t(G) \geq b(G)$ for any $G$, and a classic result of Mantel from 1907...
We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (type 1) is the class of cover times approximated by the maximal hitting times s...
A path in an edge-colored graph is called a rainbow path if all edges on it have pairwise distinct colors. For k ≥ 1, the rainbow-k-connectivity of a graph G, denoted rck(G), is the minimum number o...
Brightwell and Winkler introduced the graph parameters warmth and mobility in the context of combinatorial statistical physics. They related both parameters to lower bounds on chromatic number. Here w...

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