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A tree decomposition is a mapping of a graph into a related tree with desirable properties that allow it to be used to efficiently compute certain properties (e.g., ...

A minimum vertex cover is a vertex cover having the smallest possible number of vertices for a given graph. The size of a minimum vertex cover of a graph G is known as the ...

The kurtosis excess of a distribution is sometimes called the excess, or excess coefficient. In graph theory, excess refers to the quantity e=n-n_l(v,g) (1) for a v-regular ...

An ordered pair (a,b) of nonnegative integers such that there is some set of a points and b edges whose removal disconnects the graph and there is no set of a-1 nodes and b ...

Every graph with n vertices and maximum vertex degree Delta(G)<=k is (k+1)-colorable with all color classes of size |_n/(k+1)_| or [n/(k+1)], where |_x_| is the floor ...

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

A hypergraph is a graph in which generalized edges (called hyperedges) may connect more than two nodes.

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

A graph with minimum vertex degree at least 5 is a line graph iff it does not contain any of the above six graphs, known in this work as Metelsky graphs, as an induced ...

A walk is a sequence v_0, e_1, v_1, ..., v_k of graph vertices v_i and graph edges e_i such that for 1<=i<=k, the edge e_i has endpoints v_(i-1) and v_i (West 2000, p. 20). ...