The 3-colorability of planar graphs without cycles of length 4, 6 and 9
نویسندگان
چکیده
In this paper, we prove that planar graphs without cycles of length 4, 6, 9 are 3-colorable.
منابع مشابه
On the 3-colorability of planar graphs without 4-, 7- and 9-cycles
In this paper, we mainly prove that planar graphs without 4-, 7and 9-cycles are 3colorable. © 2009 Elsevier B.V. All rights reserved.
متن کاملPlanar graphs without adjacent cycles of length at most seven are 3-colorable
We prove that every planar graph in which no i-cycle is adjacent to a j-cycle whenever 3 ≤ i ≤ j ≤ 7 is 3-colorable and pose some related problems on the 3-colorability of planar graphs.
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.
متن کامل3-choosability of Planar Graphs with ( 4)-cycles Far Apart
A graph is k-choosable if it can be colored whenever every vertex has a list of at least k available colors. We prove that if cycles of length at most four in a planar graph G are pairwise far apart, then G is 3-choosable. This is analogous to the problem of Havel regarding 3-colorability of planar graphs with triangles far apart.
متن کاملPlanar Graphs without Cycles of Speciic Lengths
It is easy to see that planar graphs without 3-cycles are 3-degenerate. Recently, it was proved that planar graphs without 5-cycles are also 3-degenerate. In this paper it is shown, more surprisingly, that the same holds for planar graphs without 6-cycles.
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عنوان ژورنال:
- Discrete Mathematics
دوره 339 شماره
صفحات -
تاریخ انتشار 2016