کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4648212 | 1342398 | 2012 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Equitable defective coloring of sparse planar graphs
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Equitable defective coloring of sparse planar graphs Equitable defective coloring of sparse planar graphs](/preview/png/4648212.png)
چکیده انگلیسی
A graph has an equitable, defective kk-coloring (an ED-kk-coloring) if there is a kk-coloring of V(G)V(G) that is defective (every vertex shares the same color with at most one neighbor) and equitable (the sizes of all color classes differ by at most one). A graph may have an ED-kk-coloring, but no ED-(k+1)(k+1)-coloring. In this paper, we prove that planar graphs with minimum degree at least 22 and girth at least 1010 are ED-kk-colorable for any integer k≥3k≥3. The proof uses the method of discharging. We are able to simplify the normally lengthy task of enumerating forbidden substructures by using Hall’s Theorem, an unusual approach.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 312, Issue 5, 6 March 2012, Pages 957–962
Journal: Discrete Mathematics - Volume 312, Issue 5, 6 March 2012, Pages 957–962
نویسندگان
Lee Williams, Jennifer Vandenbussche, Gexin Yu,