Szekeres snark
Encyclopedia
In the mathematical
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 field of graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...

, the Szekeres snark is a snark
Snark (graph theory)
In the mathematical field of graph theory, a snark is a connected, bridgeless cubic graph with chromatic index equal to 4. In other words, it is a graph in which every vertex has three neighbors, and the edges cannot be colored by only three colors without two edges of the same color meeting at a...

 with 50 vertices
Vertex (graph theory)
In graph theory, a vertex or node is the fundamental unit out of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges , while a directed graph consists of a set of vertices and a set of arcs...

 and 75 edges. It was the fifth known snark, discovered by George Szekeres
George Szekeres
George Szekeres AM was a Hungarian-Australian mathematician.-Early years:Szekeres was born in Budapest, Hungary as Szekeres György and received his degree in chemistry at the Technical University of Budapest. He worked six years in Budapest as an analytical chemist. He married Esther Klein in 1936...

 in 1973.

As a snark, the Szekeres graph is a connected, bridgeless cubic graph
Cubic graph
In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs....

 with chromatic index equal to 4. The Szekeres snark is non-planar
Planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints...

 and non-hamiltonian but is hypohamiltonian
Hypohamiltonian graph
In the mathematical field of graph theory, a graph G is said to be hypohamiltonian if G does not itself have a Hamiltonian cycle but every graph formed by removing a single vertex from G is Hamiltonian.-History:...

.

Another well known snark on 50 vertices is the Watkins snark
Watkins snark
In the mathematical field of graph theory, the Watkins snark is a snark with 50 vertices and 75 edges. It was discovered by John J. Watkins in 1989.As a snark, the Watkins graph is a connected, bridgeless cubic graph with chromatic index equal to 4...

discovered by John J. Watkins in 1989.
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