• Discrete Applied Mathematics
• 2012
A coloring c of a graph G = (V,E) is a b-coloring if in every color class there is a vertex whose neighborhood intersects every other color classes. The b-chromatic number of G, denoted χb(G), is the(More)
• Electronic Notes in Discrete Mathematics
• 2009
A b-colouring of a graph G is a proper colouring of G such that each colour contains a vertex that is adjacent to all other colours and the b-chromatic number χb(G) is the maximum number of colours(More)
• Discrete Mathematics
• 2013
Let f(k) be the smallest integer such that every f(k)-chromatic digraph contains every oriented tree of order k. Burr proved that f(k) ≤ (k−1) and conjectured f(k) = 2n−2. In this paper, we give some(More)
• Discrete Mathematics
• 1997
Two non-adjacent vertices x and y in a graph G form an even pair if every induced path between them has an even number of edges. For a given pair fx; yg in a graph G, we denote by G xy the graph(More)
• Discrete Applied Mathematics
• 2009
A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes. The b-chromatic number of a graph G is the largest(More)
• J. Comb. Theory, Ser. B
• 1998
An even pair in a graph is a pair of non-adjacent vertices such that every chordless path between them has even length. A graph is called strict quasi-parity when every induced subgraph that is not a(More)