A sufficient condition for planar graphs to be 3-colorable
نویسندگان
چکیده
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 intersecting triangles. r 2002 Elsevier Science (USA). All rights reserved.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 88 شماره
صفحات -
تاریخ انتشار 2003