Planar Graphs Have Exponentially Many 3-Arboricities
نویسندگان
چکیده
منابع مشابه
Planar Graphs Have Exponentially Many 3-Arboricities
It is well-known that every planar or projective planar graph can be 3-colored so that each color class induces a forest. This bound is sharp. In this paper, we show that there are in fact exponentially many 3-colorings of this kind for any (projective) planar graph. The same result holds in the setting of 3-list-colorings.
متن کاملDo Triangle-Free Planar Graphs have Exponentially Many $3$-Colorings?
Thomassen conjectured that triangle-free planar graphs have an exponential number of 3-colorings. We show this conjecture to be equivalent to the following statement: there exists a positive real α such that whenever G is a planar graph and A is a subset of its edges whose deletion makes G triangle-free, there exists a subset A′ of A of size at least α|A| such that G− (A\A′) is 3-colorable. Thi...
متن کاملSub-exponentially many 3-colorings of triangle-free planar graphs
Thomassen conjectured that every triangle-free planar graph on n vertices has exponentially many 3-colorings, and proved that it has at least 2 1/12/20000 distinct 3-colorings. We show that it has at least 2 √ n/362 distinct 3-colorings. April 2010, revised 8 July 2010. An extended abstract of this paper appeared in [1]. Partially supported by an NSF Graduate Research Fellowship. Partially supp...
متن کاملExponentially many 5-list-colorings of planar graphs
We prove that every planar graph with n vertices has at least 2n/9 distinct list-colorings provided every vertex has at least five available colors. © 2006 Elsevier Inc. All rights reserved.
متن کاملSparse Graphs Usually Have Exponentially Many Optimal Colorings
A proper coloring of a graph G = (V,E) is called optimal if the number of colors used is the minimal possible; i.e., it coincides with the chromatic number of G. We investigate the typical behavior of the number of distinct optimal colorings of a random graph G(n, p), for various values of the edge probability p = p(n). Our main result shows that for every constant 1/3 < a < 2, most of the grap...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2012
ISSN: 0895-4801,1095-7146
DOI: 10.1137/110846828