5 papers
On the number of distinct spanning trees in pseudorandom graphs
Yiting Wang
A celebrated result of Otter says the number of distinct unlabelled spanning trees in is up to subexponential factors for an absolute constant . In this note, we…
Hitting time for Hamilton cycles in pseudorandom graphs
Yaobin Chen, Yu Chen, Seonghyuk Im +1
Consider the random subgraph process on a base graph with vertices: we generate a sequence by taking a uniformly random ordering of the edges of $G…
Note on the trace of random walks on pseudorandom graphs
Yaobin Chen, Yiting Wang
We study the graph-theoretic properties of the trace of random walks on pseudorandom graphs. We show that for any , there exists a constant such that the cover t…
Approximate Itai-Zehavi conjecture for random graphs
Lawrence Hollom, Lyuben Lichev, Adva Mond +2
A famous conjecture by Itai and Zehavi states that, for every -vertex-connected graph and every vertex in , there are spanning trees of such that, for every v…
Monotonicity and decompositions of random regular graphs
Lawrence Hollom, Lyuben Lichev, Adva Mond +2
In this work we establish several monotonicity and decomposition results in the framework of random regular graphs. Among other results, we show that, for a wide range of parameter…