Planar graphs without 4-, 5- and 8-cycles are 3-colorable
نویسنده
چکیده
In this paper we prove that every planar graph without 4, 5 and 8-cycles is 3-colorable.
منابع مشابه
A sufficient condition for planar graphs to be 3-colorable
Planar graphs without 3-cycles at distance less than 4 and without 5-cycles are proved to be 3-colorable. We conjecture that, moreover, each plane graph with neither 5-cycles nor intersecting 3-cycles is 3-colorable. In this conjecture, none of the two assumptions can be dropped because there exist planar 4-chromatic graphs without 5-cycles, as well as planar 4chromatic graphs without intersect...
متن کاملA note on 3-choosability of planar graphs without certain cycles
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.
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Planar graphs without cycles of length from 4 to 7 are proved to be 3-colorable. Moreover, it is proved that each proper 3-coloring of a face of length from 8 to 11 in a connected plane graph without cycles of length from 4 to 7 can be extended to a proper 3-coloring of the whole graph. This improves on the previous results on a long standing conjecture of Steinberg. © 2004 Elsevier Inc. All ri...
متن کاملThe 3-colorability of planar graphs without cycles of length 4, 6 and 9
In this paper, we prove that planar graphs without cycles of length 4, 6, 9 are 3-colorable.
متن کاملA 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...
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ورودعنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 31 شماره
صفحات -
تاریخ انتشار 2011