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On classes of graphs defined by special cutsets of lines

Part of the Lecture Notes in Mathematics book series (LNM,volume 110)

Abstract

In this paper we present a new method for studying graphs. Generally speaking this involves decomposing a graph into two disjoint subgraphs which are connected by special sets of lines. We consider four types of connections between these subgraphs, i.e., those for which the set of connecting lines describes a function, a homomorphism, a permutation, or an automorphism.

We consider this manner of decomposing a graph to be useful for studying a wide variety of parameters and properties of graphs. To illustrate this we obtain results relating to such concepts as arboricity, thickness, biparticity, and chromatic number. We derive a method for constructing new classes of critical graphs and obtain several isomorphism theorems for classes of permutation graphs, one of which involves the group theoretic concept of a double coset.

Keywords

  • Chromatic Number
  • Color Versus
  • Function Graph
  • Color Classis
  • Double Coset

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Research supported in part by the Office of Naval Research, Contract Number NR 043-367.

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References

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© 1969 Springer-Verlag

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Hedetniemi, S. (1969). On classes of graphs defined by special cutsets of lines. In: Chartrand, G., Kapoor, S.F. (eds) The Many Facets of Graph Theory. Lecture Notes in Mathematics, vol 110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060115

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  • DOI: https://doi.org/10.1007/BFb0060115

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04629-5

  • Online ISBN: 978-3-540-36161-9

  • eBook Packages: Springer Book Archive