Acta Applicandae Mathematica

, Volume 76, Issue 1, pp 57–88 | Cite as

Special Classes of Snarks

  • A. Cavicchioli
  • T. E. Murgolo
  • B. Ruini
  • F. Spaggiari

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.

simple cubic graphs chromatic index girth cyclic edge-connectivity snarks almost-Hamiltonian snarks hypo-Hamiltonian snarks critical snarks irreducible snarks total colorings total chromatic number flows computer algorithm 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • A. Cavicchioli
    • 1
  • T. E. Murgolo
    • 2
  • B. Ruini
    • 2
  • F. Spaggiari
    • 2
  1. 1.Dipartimento di Matematica Pura ed ApplicataUniversità di Modena e Reggio EmiliaModenaItaly
  2. 2.Dipartimento di Matematica Pura ed ApplicataUniversità di Modena e Reggio EmiliaModenaItaly

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