An equivalence graph is a disjoint union of cliques, and the equivalence number eq(G) of a graph G is the minimum number of equivalence subgraphs needed to cover the edges of G. W...
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 ...
In this paper we study the performance of a particular on-line coloring algorithm, the First-Fit or Greedy algorithm, on a class of perfect graphs namely the permutation graphs. W...
A graph is chordal if it does not contain any induced cycle of size greater than three. An alternative characterization of chordal graphs is via a perfect elimination ordering, whi...
A graph is Y Y reducible if it can be reduced to isolated vertices by a sequence of series-parallel reductions and Y Y transformations. It is still an open problem to characterize...