کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4650432 | 1342487 | 2008 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On Ks,tKs,t-minors in graphs with given average degree
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: On Ks,tKs,t-minors in graphs with given average degree On Ks,tKs,t-minors in graphs with given average degree](/preview/png/4650432.png)
چکیده انگلیسی
Let D(H)D(H) be the minimum d such that every graph G with average degree d has an H -minor. Myers and Thomason found good bounds on D(H)D(H) for almost all graphs H and proved that for ‘balanced’ H random graphs provide extremal examples and determine the extremal function. Examples of ‘unbalanced graphs’ are complete bipartite graphs Ks,tKs,t for a fixed s and large t . Myers proved upper bounds on D(Ks,t)D(Ks,t) and made a conjecture on the order of magnitude of D(Ks,t)D(Ks,t) for a fixed s and t→∞t→∞. He also found exact values for D(K2,t)D(K2,t) for an infinite series of t. In this paper, we confirm the conjecture of Myers and find asymptotically (in s ) exact bounds on D(Ks,t)D(Ks,t) for a fixed s and large t.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 308, Issue 19, 6 October 2008, Pages 4435–4445
Journal: Discrete Mathematics - Volume 308, Issue 19, 6 October 2008, Pages 4435–4445
نویسندگان
Alexandr Kostochka, Noah Prince,