Circular chromatic numbers of Mycielski's graphs

Chang, Gerard J.; Huang, Lingling; Zhu, Xuding

doi:10.1016/s0012-365x(99)00033-3

Cited by 57 publications

(57 citation statements)

References 21 publications

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“…The problem of calculating the circular chromatic number of Mycielski's graphs has been investigated in [4,3,7]. It turns out that the circular chromatic number of M (G) is not determined by the circular chromatic number of G alone.…”

Section: This Paper Gives Another Sufficient Condition For Graphs To mentioning

confidence: 99%

“…The problem of determining the circular chromatic number of the iterated Mycielskian of complete graphs was discussed in [3]. It was conjectured in [3] that if…”

Section: This Paper Gives Another Sufficient Condition For Graphs To mentioning

confidence: 99%

“…With complicated arguments, the special cases t = 1, 2 of this conjecture have been proved in [3,4]. A simpler proof of these special cases was given in [4] (for t = 2, the result proved in [4] is slightly weaker, i.e., it was proved in [4] …”

Section: This Paper Gives Another Sufficient Condition For Graphs To mentioning

confidence: 99%

“…For the circular chromatic number of the iterated Mycielskian of complete graphs, the following was conjectured in [3]:…”

Section: Some Improvementsmentioning

confidence: 99%

“…Corollary 10 shows that for any t ≥ 1, the integer n(t) exists and n(t) ≤ 2 t+1 − 1. It was shown in [3] that n(t) ≥ t + 2. Therefore we have…”

Section: Some Improvementsmentioning

confidence: 99%

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Circular chromatic number and Mycielski construction

Hajiabolhassan

Zhu

2003

Journal of Graph Theory

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Section: This Paper Gives Another Sufficient Condition For Graphs To mentioning

confidence: 99%

“…The problem of determining the circular chromatic number of the iterated Mycielskian of complete graphs was discussed in [3]. It was conjectured in [3] that if…”

Section: This Paper Gives Another Sufficient Condition For Graphs To mentioning

confidence: 99%

Section: This Paper Gives Another Sufficient Condition For Graphs To mentioning

confidence: 99%

“…For the circular chromatic number of the iterated Mycielskian of complete graphs, the following was conjectured in [3]:…”

Section: Some Improvementsmentioning

confidence: 99%

“…Corollary 10 shows that for any t ≥ 1, the integer n(t) exists and n(t) ≤ 2 t+1 − 1. It was shown in [3] that n(t) ≥ t + 2. Therefore we have…”

Section: Some Improvementsmentioning

confidence: 99%

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Circular chromatic number and Mycielski construction

Hajiabolhassan

Zhu

2003

Journal of Graph Theory

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The circular chromatic number of the Mycielskian ofGdk

Huang

Chang

1999

J. Graph Theory

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In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph G into a new graph µ(G), we now call the Mycielskian of G, which has the same clique number as G and whose chromatic number equals χ(G)+1. Chang, Huang, and Zhu [G. J. Chang, L. Huang, & X. Zhu, Discrete Math, to appear] have investigated circular chromatic numbers of Mycielskians for several classes of graphs. In this article, we study circular chromatic numbers of Mycielskians for another class of graphs G d k . The main result is that χ c (µ(G d k )) = χ(µ(G d k )), which settles a problem raised in [G. J. Chang, L. Huang, & X. Zhu, Discrete Math, to appear, and X. Zhu, to appear]. As χ c (G d k ) = k d and χ(G d k ) = k d , consequently, there exist graphs G such that χ c (G) is as close to χ(G) − 1 as you want, but χ c (µ(G)) = χ(µ(G)).

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