We consider the problem of periodic exploration of all nodes in undirected graphs by using a nite state automaton called later a robot. The robot, using a constant number of state...
Leszek Gasieniec, Ralf Klasing, Russell A. Martin,...
For a graph G and k a real number, we consider the sum of the k-th powers of the degrees of the vertices of G. We present some general bounds on this sum for various values of k. ...
We study the following two functions: d(n, c) and d(n, c); d(n, c) (d(n, c)) is the minimum number k such that every c-edge-colored undirected (directed) graph of order n and mini...
We exhibit a a counterexample to a conjecture of Thomassen stating that the number of distinct 3-colorings of every graph whose 3color matrix has full column rank is superpolynomi...
We prove that for every k and every ε > 0, there exists g such that every graph with tree-width at most k and odd-girth at least g has circular chromatic number at most 2 + ε...