منابع مشابه
The smallest nonevasive graph property
A property of n-vertex graphs is called evasive if every algorithm testing this property by asking questions of the form “is there an edge between vertices u and v” requires, in the worst case, to ask about all pairs of vertices. Most “natural” graph properties are either evasive or conjectured to be such, and of the few examples of nontrivial nonevasive properties scattered in the literature t...
متن کاملThe Petersen graph is the smallest 3-cop-win graph
In the game of cops and robbers on a graph G = (V,E), k cops try to catch a robber. On the cop turn, each cop may move to a neighboring vertex or remain in place. On the robber’s turn, he moves similarly. The cops win if there is some time at which a cop is at the same vertex as the robber. Otherwise, the robber wins. The minimum number of cops required to catch the robber is called the cop num...
متن کاملOn the smallest 3-cop win graph
In the game of cops and robbers on a graph G = (V,E), k cops try to catch a robber. On the cop turn, each cop may move to a neighboring vertex or remain in place. On the robber’s turn, he moves similarly. The cops win if there is some time at which a cop is at the same vertex as the robber. Otherwise, the robber wins. The minimum number of cops required to catch the robber is called the cop num...
متن کاملThe smallest hard-to-color graph for the SL algorithm
For a given approximate vertex coloring algorithm a graph is said to be slightly hard-tocolor (SHC) if some implementation of the algorithm uses more colors than the minimum needed. Similarly, a graph is said to be hard-to-color (HC) if every implementation of the algorithm results in a nonoptimal coloring. We study smallest such graphs for the smallest-last (SL) coloring algorithm. Our main re...
متن کاملA characterization of the smallest eigenvalue of a graph
It is well known that the smallest eigenvalue of the adjacency matrix of a connected ¿-regular graph is at least -d and is strictly greater than -d if the graph is not bipartite. More generally, for any connected graph G = (V JE), consider the matrix Q = D + A where D is the diagonal matrix of degrees in the graph G , and A is the adjacency matrix of G . Then Q is positive semi-definite, and th...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2014
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1766