Circular coloring and Mycielski construction
نویسندگان
چکیده
In this paper, we investigate circular chromatic number of Mycielski construction of graphs. It was shown in [20] that t Mycielskian of the Kneser graph KG(m,n) has the same circular chromatic number and chromatic number provided that m + t is an even integer. We prove that if m is large enough, then χ(M (KG(m,n))) = χc(M (KG(m,n))) where M t is t Mycielskian. Also, we consider the generalized Kneser graph KG(m,n, s) and show that there exists a threshold m(n, s, t) such that χ(M (KG(m,n, s))) = χc(M (KG(m,n, s))) for m ≥ m(n, s, t).
منابع مشابه
Circular chromatic number and Mycielski construction
This paper gives a sufficient condition for a graph G to have its circular chromatic number equal its chromatic number. By using this result, we prove that for any integer t ≥ 1, there exists an integer n such that for all k ≥ n χc(M (Kk)) = χ(M (Kk)).
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 310 شماره
صفحات -
تاریخ انتشار 2010