Snark Conjecture
In the mathematics, mathematical field of graph theory, a snark is an undirected graph with cubic graph, exactly three edges per vertex whose edge coloring, edges cannot be colored with only three colors. In order to avoid trivial cases, snarks are often restricted to have additional requirements on their Connectivity (graph theory), connectivity and on Girth (graph theory), the length of their cycles. Infinitely many snarks exist. One of the equivalent forms of the four color theorem is that every snark is a planar graph, non-planar graph. Research on snarks originated in Peter G. Tait's work on the four color theorem in 1880, but their name is much newer, given to them by Martin Gardner in 1976. Beyond coloring, snarks also have connections to other hard problems in graph theory: writing in the ''Electronic Journal of Combinatorics'', Miroslav Chladný and Martin Škoviera state that As well as the problems they mention, W. T. Tutte's ''snark conjecture'' concerns the exist ...
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