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Chromatic number and subgraphs of cayley graphs

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Book cover Theory and Applications of Graphs

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 642))

Abstract

Results, problems and conjectures concerning the chromatic number and subgraphs of finite and infinite Cayley graphs are presented. We prove that every group has a Cayley graph of chromatic number ≤ ω; for solvable groups the minimum chromatic number is ≤ 3. The Cayley graph of an irreducible group presentation contains neither K3,5 nor K −4 as a subgraph. Every group has a Cayley graph containing neither K −4 nor K5,17. We mention that every graph is a induced subgraph of some Cayley graph of any sufficiently large group.

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Author information

Authors and Affiliations

  1. Eötvös L. University, Budapest, Hungary

    László Babai

Authors
  1. László Babai
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Western Michigan University, Kalamazoo, MI, 49008, USA

    Yousef Alavi  & Don R. Lick  & 

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© 1978 Springer-Verlag Berlin Heidelberg

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Babai, L. (1978). Chromatic number and subgraphs of cayley graphs. In: Alavi, Y., Lick, D.R. (eds) Theory and Applications of Graphs. Lecture Notes in Mathematics, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070361

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  • DOI: https://doi.org/10.1007/BFb0070361

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08666-6

  • Online ISBN: 978-3-540-35912-8

  • eBook Packages: Springer Book Archive

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