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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 ...

An arc of a graph, sometimes also called a flag, is an ordered pair of adjacent vertices (Godsil and Royle 2001, p. 59), sometimes also called a directed line (Harary 1994, ...

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 lower matching number of a graph is the minimum size of a maximal independent edge set. The (upper) matching number may be similarly defined as the largest size of an ...

A tree not having the complete bipartite graph K_(1,2) with base at the vertex of degree two as a limb (Lu et al. 1993, Lu 1996).

The maximum flow between vertices v_i and v_j in a graph G is exactly the weight of the smallest set of edges to disconnect G with v_i and v_j in different components (Ford ...

The middle levels conjecture, also known as revolving door conjecture, posits that the middle layer graph has a Hamilton cycle for every n>=1. The conjecture was proved by ...

A minimal edge cover is an edge cover of a graph that is not a proper subset of any other edge cover. Every minimum edge cover is a minimal edge cover, but the converse does ...

A minimal vertex cut is an vertex cut of a graph that is not a proper subset of any other vertex cut. Every minimum vertex cut is a minimal vertex cut, but the converse does ...

The vector field N_f(z)=-(f(z))/(f^'(z)) arising in the definition of the Newtonian graph of a complex univariate polynomial f (Smale 1985, Shub et al. 1988, Kozen and ...