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Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...

A column-convex polyomino is a self-avoiding convex polyomino such that the intersection of any vertical line with the polyomino has at most two connected components. ...

The geodesics in a complete Riemannian metric go on indefinitely, i.e., each geodesic is isometric to the real line. For example, Euclidean space is complete, but the open ...

Pairs of partitions for a single number whose Ferrers diagrams transform into each other when reflected about the line y=-x, with the coordinates of the upper left dot taken ...

Connect-Four is a tic-tac-toe-like two-player game in which players alternately place pieces on a vertical board 7 columns across and 6 rows high. Each player uses pieces of ...

A constant function is function f(x)=c whose value does not change as its parameters vary. The function graph of a one-dimensional constant function is a straight line. The ...

Conway's soldiers, also known as the "solitaire army" game (Berlekamp et al. 1982) or "checker-jumping problem" (Honsberger 1976) is a one-player game played on an infinite ...

A cross-handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in the ...

There are several attractive polyhedron compounds consisting of three cubes. The first (left figures) arises by joining three cubes such that each shares two C_2 axes (Holden ...