A well-known theorem of Mader [5] states that highly connected subgraphs can be forced in finite graphs by assuming a high minimum degree. Solving a problem of Diestel [2], we ex...
In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...
Graphical games have been proposed as a game-theoretic model of large-scale distributed networks of non-cooperative agents. When the number of players is large, and the underlying...
Edith Elkind, Leslie Ann Goldberg, Paul W. Goldber...
A spanning subgraph G of a graph H is a k-detour subgraph of H if for each pair of vertices x, y V (H), the distance, distG(x, y), between x and y in G exceeds that in H by at mo...
Nana Arizumi, Peter Hamburger, Alexandr V. Kostoch...
Let G = (V, E) be a graph. Let c : V → N be a vertex-coloring of the vertices of G. For any vertex u, we denote by N[u] its closed neighborhood (u and its adjacent vertices), an...