کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4649943 | 1342471 | 2008 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The minimum number of vertices for a triangle-free graph with χl(G)=4χl(G)=4 is 11
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
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چکیده انگلیسی
It is well-known that the minimum number of vertices for a triangle-free 4-chromatic graph is 11, and the Grötzsch graph is just such a graph. In this paper, we show that every non-bipartite triangle-free graph GG of order not greater than 10 has χl(G)=3χl(G)=3. Combined with a known result by Hanson et al. [D. Hanson, G. MacGillivray, B. Toft, Choosability of bipartite graphs, Ars Combin. 44 (1996) 183–192] that every bipartite graph of order not greater than 13 is 3-choosable, we conclude that the minimum number of vertices for a triangle-free graph with χl(G)=4χl(G)=4 is also 11.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 308, Issue 23, 6 December 2008, Pages 5342–5348
Journal: Discrete Mathematics - Volume 308, Issue 23, 6 December 2008, Pages 5342–5348
نویسندگان
Baoyindureng Wu, Li Zhang,