Consider random regular graphs of order n and degree d = d(n) 3. Let g = g(n) 3 satisfy (d-1)2g-1 = o(n). Then the number of cycles of lengths up to g have a distribution simila...
Brendan D. McKay, Nicholas C. Wormald, Beata Wysoc...
A proper coloring of the edges of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a (G), is the least number of...
In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dom...
We consider instances of the maximum independent set problem that are constructed according to the following semirandom model. Let Gn,p be a random graph, and let S be a set consis...
A method that utilizes the polynomially solvable critical independent set problem for solving the maximum independent set problem on graphs with a nonempty critical independent se...