A note on 3-choosability of planar graphs without certain cycles

نویسندگان

Li Zhang

Baoyindureng Wu

چکیده

Steinberg asked whether every planar graph without 4 and 5 cycles is 3-colorable. Borodin, and independently Sanders and Zhao, showed that every planar graph without any cycle of length between 4 and 9 is 3-colorable. We improve this result by showing that every planar graph without any cycle of length 4, 5, 6, or 9 is 3-choosable. © 2005 Elsevier B.V. All rights reserved.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A note on the not 3-choosability of some families of planar graphs

A graph G is L-list colorable if for a given list assignment L= {L(v): v ∈ V }, there exists a proper coloring c of G such that c(v) ∈ L(v) for all v ∈ V . If G is L-list colorable for any list assignment with |L(v)| k for all v ∈ V , then G is said k-choosable. In [M. Voigt, A not 3-choosable planar graph without 3-cycles, Discrete Math. 146 (1995) 325–328] and [M. Voigt, A non-3choosable plan...

متن کامل

On Choosability with Separation of Planar Graphs with Forbidden Cycles

We study choosability with separation which is a constrained version of list coloring of graphs. A (k, d)-list assignment L of a graph G is a function that assigns to each vertex v a list L(v) of at least k colors and for any adjacent pair xy, the lists L(x) and L(y) share at most d colors. A graph G is (k, d)-choosable if there exists an L-coloring of G for every (k, d)-list assignment L. This...

متن کامل

Choosability and edge choosability of planar graphs without five cycles

It is proved that a planar graph G without five cycles is three degenerate, hence, four choosable, and it is also edge-(A( G) + l)h c oosable. @ 2002 Elsevier Science Ltd. All rights reserved. Keywords-Choosability, Edge choosability, Degeneracy, Planar graph.

متن کامل

Bounds on circular consecutive choosability

The circular consecutive choosability chcc(G) of a graph G has been recently introduced in [2]. In this paper we prove upper bounds on chcc for series-parallel graphs, planar graphs and k-choosable graphs. Our bounds are tight for classes of series-parallel graphs and k-choosable graphs for k ≥ 3. Then we study the circular consecutive choosability of generalized theta graphs. Lower bounds for ...

متن کامل