منابع مشابه
Group Colorability of Graphs
Let G = (V,E) be a graph and A a non-trivial Abelian group, and let F (G,A) denote the set of all functions f : E(G) → A. Denote by D an orientation of E(G). Then G is A-colorable if and only if for every f ∈ F (G,A) there exists an A-coloring c: V (G) → A such that for every e = (x, y) ∈ E(G) (assumed to be directed from x to y), c(x) − c(y) 6= f(e). If G is a graph, we define its group chroma...
متن کاملGroup colorability of multigraphs
Let G be a multigraph with a fixed orientation D and let Γ be a group. Let F(G, Γ ) denote the set of all functions f : E(G) → Γ . A multigraph G is Γ -colorable if and only if for every f ∈ F(G, Γ ), there exists a Γ -coloring c : V (G) → Γ such that for every e = uv ∈ E(G) (assumed to be directed from u to v), c(u)c(v)−1 ≠ f (e). We define the group chromatic number χg (G) to be the minimum i...
متن کاملColorability Saturation Games
We consider the following two-player game: Maxi and Mini start with the empty graph on n vertices and take turns, always adding one additional edge to the graph such that the chromatic number is at most k, where k ∈ N is a given parameter. The game is over when the graph is saturated and no further edge can be inserted. Maxi wants to maximize the length of the game while Mini wants to minimize ...
متن کاملTesting k-colorability
Let G be a graph on n vertices and suppose that at least n edges have to be deleted from it to make it k-colorable. It is shown that in this case most induced subgraphs of G on ck ln k/ 2 vertices are not k-colorable, where c > 0 is an absolute constant. If G is as above for k = 2, then most induced subgraphs on (ln(1/ )) b are non-bipartite, for some absolute positive constant b, and this is t...
متن کاملExploring k-Colorability
The P vs NP problem is now well-known worldwide, even beyond academia, due to the publicity generated by the Clay Mathematics Institute, which bestowed upon it one of seven Millennium Prizes on a correct proof of the solution. The concept of NP-completeness was first formulated by Stephen Cook, in application to the boolean satisfiability problem [Coo71]. Later, Richard Karp took 20 additional ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1987
ISSN: 0024-3795
DOI: 10.1016/0024-3795(87)90079-6