The Turán number of disjoint copies of paths

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• 作者：Long-Tu Yuan ^{yuanlongtu@sjtu.edu.cn} ; Xiao-Dong Zhang ; ^{xiaodong@sjtu.edu.cn}
• 关键词：Tur&aacute ; n number ; Extremal graph ; Disjoint path
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：6 February 2017
• 年：2017
• 卷：340
• 期：2
• 页码：132-139
• 全文大小：410 K
• 卷排序：340

文摘

The Turán number of a graph HH, denoted by ex(n,H)ex(n,H), is the maximum number of edges in a simple graph of order nn which does not contain HH as a subgraph. In this paper, we determine the value ex(n,k⋅P3) and characterize all extremal graphs for all positive integers nn and kk, where k⋅P3 is kk disjoint copies of a path on three vertices. This extends a result of Bushaw and Kettle (2011), which solved the conjecture proposed by Gorgol (2011).