【摘 要】
：
A 2-graph is a hypergraph with edge sizes of at most two. A regular 2-graph is said to be minimal if it does not contain a proper regular factor. Let f2(n) be t
【机 构】
：
Department of Physics and Computer Science,School of Mathematics and System Science,Department of Ma
【基金项目】
：
高等学校博士学科点专项科研基金;国家自然科学基金;the Natural Sciences and Engineering Research Council of Canada
论文部分内容阅读
A 2-graph is a hypergraph with edge sizes of at most two. A regular 2-graph is said to be minimal if it does not contain a proper regular factor. Let f2(n) be the maximum value of degrees over all minimal regular 2-graphs of n vertices. In this paper, we provide a structure property of minimal regular 2-graphs, and consequently, prove that f2(n) = n+3-i/3where 1 ≤i≤6, i=n (mod 6) andn≥ 7, which solves a conjecture posed by Fan, Liu, Wu and Wong. As applications in graph theory, we are able to characterize unfactorable regular graphs and provide the best possible factor existence theorem on degree conditions. Moreover, f2(n) and the minimal 2-graphs can be used in the universal switch box designs, which originally motivated this study.
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