• Discrete Mathematics
• 1997
Let G = (V,E) be a connected undirected graph. For any vertex v âˆˆ V , the closed neighborhood of v is N [v] = {v} âˆª {u âˆˆ V | uv âˆˆ E }. For S âŠ† V , the closed neighborhood of S is N [S] = â‹ƒ vâˆˆS N [v].â€¦ (More)
• Discrete Applied Mathematics
• 2006
We say that a function f : V â†’ {0, 1, . . . , diam(G)} is a broadcast if for every vertex v âˆˆ V , f(v) â‰¤ e(v), where diam(G) denotes the diameter of G and e(v) denotes the eccentricity of v. The costâ€¦ (More)
• Discrete Mathematics
• 1999
We introduce one of many classes of problems which can be defined in terms of 3-valued functions on the vertices of a graph G = (V, E) of the form f : V + { 1, 0, l}. Such a fknction is said to be aâ€¦ (More)
• Discrete Mathematics
• 1995
In a graph G = (V; E), a set of vertices S is nearly perfect if every vertex in V ? S is adjacent to at most one vertex in S. Nearly perfect sets are closely related to 2-packings of graphs, stronglyâ€¦ (More)
• Discussiones Mathematicae Graph Theory
• 1998
Let Ï„(G) denote the number of vertices in a longest path of the graph G and let k1 and k2 be positive integers such that Ï„(G) = k1+k2. The question at hand is whether the vertex set V (G) can beâ€¦ (More)
• Discussiones Mathematicae Graph Theory
• 2005
The Directed Path Partition Conjecture is the following: If D is a digraph that contains no path with more than Î» vertices then, for every pair (a, b) of positive integers with Î» = a + b, thereâ€¦ (More)