We prove that the crossing number of a graph decays in a “continuous fashion” in the following sense. For any ε > 0 there is a δ > 0 such that for n sufficiently large...
In the framework of parameterized complexity, exploring how one parameter affects the complexity of a different parameterized (or unparameterized problem) is of general interest....
Erdos proved that there are graphs with arbitrarily large girth and chromatic number. We study the extension of this for generalized chromatic numbers. Generalized graph coloring d...
Let β(G), Γ(G) and IR(G) be the independence number, the upper domination number and the upper irredundance number, respectively. A graph G is called Γperfect if β(H) = Γ(H),...
: 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...