We study vertex-colorings of plane graphs that do not contain a rainbow face, i.e., a face with vertices of mutually distinct colors. If G is a 3-connected plane graph with n vert...
The problem of computing the chromatic number of a P5-free graph (a graph which contains no path on 5 vertices as an induced subgraph) is known to be NP-hard. However, we show tha...
It is proven that for every fixed h, a and b, a graph with n vertices and minimum degree at least h-1 h n, which contains no copy of Kb (the complete graph with b vertices), conta...
Let P be the point set in two dimensional plane. In this paper, we consider the problem of locating two isothetic unit squares such that together they cover maximum number of poin...
Priya Ranjan Sinha Mahapatra, Partha P. Goswami, S...
We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number gn of unlabeled outerplanar graphs on n vertices can be computed in polynomial time,...