On the theta number of powers of cycle graphs


We give a closed formula for Lovász’s theta number of the powers of cycle graphs C d−1 k and of their complements, the circular complete graphs K k/d . As a consequence, we establish that the circular chromatic number of a circular perfect graph is computable in polynomial time. We also derive an asymptotic estimate for the theta number of C d k .

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Correspondence to Christine Bachoc.

Additional information

Supported by the ANR/NSC project GraTel ANR-09-blan-0373-01, NSC98-2115-M-002-013-MY3 and NSC99-2923-M-110-001-MY3.

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Bachoc, C., Pêcher, A. & Thiéry, A. On the theta number of powers of cycle graphs. Combinatorica 33, 297–317 (2013). https://doi.org/10.1007/s00493-013-2950-x

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Mathematics Subject Classification (2000)

  • 05C15
  • 05C85
  • 90C27