کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4647894 | 1342382 | 2012 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
(k,1)(k,1)-coloring of sparse graphs
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
A graph GG is (k,1)(k,1)-colorable if the vertex set of GG can be partitioned into subsets V1V1 and V2V2 such that the graph G[V1]G[V1] induced by the vertices of V1V1 has maximum degree at most kk and the graph G[V2]G[V2] induced by the vertices of V2V2 has maximum degree at most 11. We prove that every graph with maximum average degree less than 10k+223k+9 admits a (k,1)(k,1)-coloring, where k≥2k≥2. In particular, every planar graph with girth at least 7 is (2,1)(2,1)-colorable, while every planar graph with girth at least 6 is (5,1)(5,1)-colorable. On the other hand, when k≥2k≥2 we construct non-(k,1)(k,1)-colorable graphs whose maximum average degree is arbitrarily close to 14k4k+1.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 312, Issue 6, 28 March 2012, Pages 1128–1135
Journal: Discrete Mathematics - Volume 312, Issue 6, 28 March 2012, Pages 1128–1135
نویسندگان
O.V. Borodin, A.O. Ivanova, M. Montassier, A. Raspaud,