In the

mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

field of

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

, 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 "Snark ...

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 B ...

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 bipa ...

with

chromatic index In graph theory, an edge coloring of a 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 coloring of a graph by the colors red, blue ...

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 into 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 o ...

3 and

queue number In the mathematical field of graph theory, the queue number of a graph is a graph invariant defined analogously to stack number (book thickness) using first-in first-out (queue) orderings in place of last-in first-out (stack) orderings. Defin ...

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 special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices o ...

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 {{combin-stub