On 3-choosable planar graphs of girth at least 4
نویسندگان
چکیده
منابع مشابه
On 3-choosable planar graphs of girth at least 4
Let G be a plane graph of girth at least 4. Two cycles of G are intersecting if they have at least one vertex in common. In this paper, we show that if a plane graph G has neither intersecting 4-cycles nor a 5-cycle intersecting with any 4-cycle, then G is 3-choosable, which extends one of Thomassen’s results [C. Thomassen, 3-list-coloring planar graphs of girth 5, J. Combin. Theory Ser. B 64 (...
متن کاملPlanar Graphs of Girth at least Five are Square (∆ + 2)-Choosable
We prove a conjecture of Dvořák, Král, Nejedlý, and Škrekovski that planar graphs of girth at least five are square (∆ + 2)-colorable for large enough ∆. In fact, we prove the stronger statement that such graphs are square (∆+2)-choosable and even square (∆+2)-paintable.
متن کاملGroup chromatic number of planar graphs of girth at least 4
Jeager et al introduced a concept of group connectivity as an generalization of nowhere zero flows and its dual concept group coloring, and conjectured that every 5-edge connected graph is Z3-connected. For planar graphs, this is equivalent to that every planar graph with girth at least 5 must have group chromatic number at most 3. In this paper we show that if G is a plane graph with girth at ...
متن کامل2-distance 4-colorability of Planar Subcubic Graphs with Girth at Least 22
The trivial lower bound for the 2-distance chromatic number χ2(G) of any graph G with maximum degree ∆ is ∆+1. It is known that χ2 = ∆+1 if the girth g of G is at least 7 and ∆ is large enough. There are graphs with arbitrarily large ∆ and g ≤ 6 having χ2(G) ≥ ∆ + 2. We prove the 2-distance 4-colorability of planar subcubic graphs with g ≥ 22.
متن کاملPlanar graphs with girth at least 5 are (3, 5)-colorable
A graph is (d1, . . . , dr )-colorable if its vertex set can be partitioned into r sets V1, . . . , Vr where themaximum degree of the graph induced by Vi is at most di for each i ∈ {1, . . . , r}. Let Gg denote the class of planar graphs with minimum cycle length at least g . We focus on graphs in G5 since for any d1 and d2, Montassier and Ochem constructed graphs in G4 that are not (d1, d2)-co...
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: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.05.055