Let H be a finite family of graphs. A graph G is H-universal if it contains a copy of each H H as a subgraph. Let H(k, n) denote the family of graphs on n vertices with maximum d...
We show that every NP problem is polynomially equivalent to a simple combinatorial problem: the membership problem for a special class of digraphs. These classes are defined by me...
A star forest is a collection of vertex-disjoint trees of depth at most 1, and its size is the number of leaves in all its components. A spanning star forest of a given graph G is ...
A colored graph is a complete graph in which a color has been assigned to each edge, and a colorful cycle is a cycle in which each edge has a different color. We first show that ...
Richard N. Ball, Ales Pultr, Petr Vojtechovsk&yacu...
For a graph G and an integer t we let mcct(G) be the smallest m such that there exists a coloring of the vertices of G by t colors with no monochromatic connected subgraph having ...