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The graph complement of a graph hole. Graph antiholes are called even if they have an even number of vertices and odd if they have an odd number of vertices (Chvátal). No odd ...

The term in rigidity theory for the edges of a graph.

The composition G=G_1[G_2] of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph with point vertex V_1×V_2 and u=(u_1,u_2) ...

The cube of a graph is defined as its third graph power.

The periphery of a graph G is the subgraph of G induced by vertices that have graph eccentricities equal to the graph diameter. The periphery of a connected graph may be ...

Assignment of each graph edge of a graph to one of two color classes (commonly designation "red" and "green").

A formula satisfied by all Hamiltonian cycles with n nodes. Let f_j be the number of regions inside the circuit with j sides, and let g_j be the number of regions outside the ...

The problem of deciding if four colors are sufficient to color any map on a plane or sphere.

A symmetric block design (4n+3, 2n+1, n) which is equivalent to a Hadamard matrix of order 4n+4. It is conjectured that Hadamard designs exist for all integers n>0, but this ...

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 ...