We report the most relevant results on the classification, up to isomorphism, of nontrivial simple uncolorable (i.e., the chromatic index equals 4) cubic graphs, called snarks in the literature. Then we study many classes of snarks satisfying certain additional conditions, and investigate the relationships among them. Finally, we discuss connections between the snark family and some significant conjectures of graph theory, and list some problems and open questions which arise naturally in this research.
Special classes of snarks / Cavicchioli, Alberto; Te, Murgolo; Ruini, Beatrice; Spaggiari, Fulvia. - In: ACTA APPLICANDAE MATHEMATICAE. - ISSN 0167-8019. - STAMPA. - 76:(2003), pp. 57-88. [10.1023/A:1022864000162]
Special classes of snarks
CAVICCHIOLI, Alberto;RUINI, Beatrice;SPAGGIARI, Fulvia
2003
Abstract
We report the most relevant results on the classification, up to isomorphism, of nontrivial simple uncolorable (i.e., the chromatic index equals 4) cubic graphs, called snarks in the literature. Then we study many classes of snarks satisfying certain additional conditions, and investigate the relationships among them. Finally, we discuss connections between the snark family and some significant conjectures of graph theory, and list some problems and open questions which arise naturally in this research.
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