Extending Fractional Precolorings
نویسندگان
چکیده
For every d ≥ 3 and k ∈ {2} ∪ [3,∞), we determine the smallest ε such that every fractional (k + ε)-precoloring of vertices at mutual distance at least d of a graph G with fractional chromatic number equal to k can be extended to a proper fractional (k + ε)-coloring of G. Our work complements the analogous results of Albertson for ordinary colorings and those of Albertson and West for circular colorings.
منابع مشابه
Extensions of Fractional Precolorings
We study the following problem: given a real number k and integer d, what is the smallest ε such that any fractional (k+ε)-precoloring of vertices at pairwise distances at least d of a fractionally k-colorable graph can be extended to a fractional (k + ε)coloring of the whole graph? The exact values of ε were known for k ∈ {2} ∪ [3,∞) and any d. We determine the exact values of ε for k ∈ (2, 3)...
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 26 شماره
صفحات -
تاریخ انتشار 2012