In the

mathematical Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

field of

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

, the Szekeres snark is a

snark Snark may refer to: Fictional creatures * Snark (Lewis Carroll), a fictional animal species in Lewis Carroll's ''The Hunting of the Snark'' (1876) * Zn'rx, a race of fictional aliens in Marvel Comics publications, commonly referred to as "Snarks ...

with 50 vertices and 75 edges. It was the fifth known snark, discovered by

George Szekeres George Szekeres AM FAA (; 29 May 1911 – 28 August 2005) 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 ...

in 1973. As a snark, the Szekeres graph is a connected, bridgeless

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. A bicubic graph is a cubic bip ...

with

chromatic index In graph theory, a proper edge coloring of a Graph (discrete mathematics), graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color. For example, the figure to the right shows an edge colorin ...

equal to 4. The Szekeres snark is non-planar and non-hamiltonian but is hypohamiltonian. It has

book thickness In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings in a ''book'', a collection of half-planes all having the same line as their boundary. Usually, the vertices of the graph are required to lie on ...

3 and queue number 2. Another well known snark on 50 vertices is the Watkins snark discovered by John J. Watkins in 1989.Watkins, J. J. "Snarks." Ann. New York Acad. Sci. 576, 606-622, 1989.

Gallery

Image:Szekeres snark 3COL.svg, The

chromatic number In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain constraints, such as that no two adjacent elements have the same color. Graph coloring i ...

of the Szekeres snark is 3. Image:Szekeres snark 4color edge.svg, The

of the Szekeres snark is 4. Image:Szekeres-snark.svg, Alternative drawing of the Szekeres snark.

References

Individual graphs Regular graphs {{Graph-stub