We prove that for all 0 ≤ t ≤ k and d ≥ 2k, every graph G with treewidth at most k has a ‘large’ induced subgraph H, where H has treewidth at most t and every vertex in ...
d Abstract) Noga Alon1, , Michael Capalbo2, , Yoshiharu Kohayakawa3, , Vojtˇech R¨odl4,† , Andrzej Ruci´nski5,‡ , and Endre Szemer´edi6,§ 1 Department of Mathematics, Raym...
Noga Alon, Michael R. Capalbo, Yoshiharu Kohayakaw...
We prove that the total chromatic number of any graph with maximum degree is at most plus an absolute constant. In particular, we show that for su ciently large, the total chromat...
We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1 − )n vertices, in terms of the expansion prop...
In this paper, we propose a simple and natural randomized algorithm to embed a tree T in a given graph G. The algorithm can be viewed as a "self-avoiding tree-indexed random ...