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 ...
Classes of graphs with bounded expansion have been introduced in [15], [12]. They generalize both proper minor closed classes and classes with bounded degree. For any class with b...
We solve an open problem posed by Eppstein in 1995 [14, 15] and re-enforced by Grohe [16, 17] concerning locally bounded treewidth in minor-closed families of graphs. A graph has ...
For a family F of graphs, a graph U is said to be F-universal if every graph of F is a subgraph of U. Similarly, a graph is said to be F-induced-universal if every graph of F is a...
: We present an improved upper bound of O(d1+ 1 m−1 ) for the (2, F)-subgraph chromatic number χ2,F (G) of any graph G of maximum degree d. Here, m denotes the minimum number of...