A Note on 3-colorable Plane Graphs without 5- and 7-cycles
نویسنده
چکیده
In [1], Borodin et al figured out a gap of [5], and gave a new proof with the similar technique. The purpose of this note is to fix the gap of [5] by slightly revising the definition of special faces, and adding a few lines of explanation in the proofs (new added text are all in black font).
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...
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ورودعنوان ژورنال:
- Discrete Math., Alg. and Appl.
دوره 1 شماره
صفحات -
تاریخ انتشار 2009