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A graph G is hypohamiltonian if G is nonhamiltonian, but G-v is Hamiltonian for every v in V (Bondy and Murty 1976, p. 61). The Petersen graph, which has ten nodes, is the ...

The fractional edge chromatic number of a graph G is the fractional analog of the edge chromatic number, denoted chi_f^'(G) by Scheinerman and Ullman (2011). It can be ...

An arrangement of overlapping circles which cover the entire plane. A lower bound for a covering using equivalent circles is 2pi/sqrt(27) (Williams 1979, p. 51).

A curve composed exclusively of circular arcs.

A connected graph G is said to be t-tough if, for every integer k>1, G cannot be split into k different connected components by the removal of fewer than tk vertices. The ...

The Descartes snarks are a set of snarks on 210 vertices and 315 edges discovered by William Tutte in 1948 writing under the pseudonym Blanche Descartes (Descartes 1948; ...

Given five equal disks placed symmetrically about a given center, what is the smallest radius r for which the radius of the circular area covered by the five disks is 1? The ...

A maximally nonhamiltonian graph is a nonhamiltonian graph G for which G+e is Hamiltonian for each edge e in the graph complement of G^_, i.e., every two nonadjacent vertices ...

One of the beautiful arrangements of circles found at the Temple of Osiris at Abydos, Egypt (Rawles 1997). The pattern also appears in Italian art from the 13th century ...

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. This partitions graphs into ...