In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs...In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs Combin. 2007].展开更多
For integers k 0, r 0, a（k, r）-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree d is adjacent to vertices with at least min{d, r} diferent colors. The r-hued chromatic nu...For integers k 0, r 0, a（k, r）-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree d is adjacent to vertices with at least min{d, r} diferent colors. The r-hued chromatic number, denoted by χr（G）, is the smallest integer k for which a graph G has a（k, r）-coloring. Define a graph G is r-normal, if χr（G） = χ（G）. In this paper, we present two sufcient conditions for a graph to be 3-normal, and the best upper bound of 3-hued chromatic number of a certain families of graphs.展开更多
In this paper, we set ρ_r =~r4^（1/2） and ρ′_r= β^（-1/r）, where β =-1/6 ·（100 ＋ 12·（69）^（1/2））^（1/3）-2/（3·（100＋12·（69）^（1/2）））^（1/3）＋4/3≈0.2451223338. We consider conn...In this paper, we set ρ_r =~r4^（1/2） and ρ′_r= β^（-1/r）, where β =-1/6 ·（100 ＋ 12·（69）^（1/2））^（1/3）-2/（3·（100＋12·（69）^（1/2）））^（1/3）＋4/3≈0.2451223338. We consider connected r-uniform hypergraphs with spectral radius between ρ_r and ρ′_r and give a description of such hypergraphs.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11601368)
文摘In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs Combin. 2007].
基金Supported by the Project of Shandong Province Higher Educational Science and Technology Program (Grant No.J10LA11)the Natural Science Foundation of Shandong Province (Grant No.ZR2010AQ003)
文摘For integers k 0, r 0, a（k, r）-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree d is adjacent to vertices with at least min{d, r} diferent colors. The r-hued chromatic number, denoted by χr（G）, is the smallest integer k for which a graph G has a（k, r）-coloring. Define a graph G is r-normal, if χr（G） = χ（G）. In this paper, we present two sufcient conditions for a graph to be 3-normal, and the best upper bound of 3-hued chromatic number of a certain families of graphs.
基金Supported by the National Natural Science Foundation of China(Grant Nos.116013681140143411771322)
文摘In this paper, we set ρ_r =~r4^（1/2） and ρ′_r= β^（-1/r）, where β =-1/6 ·（100 ＋ 12·（69）^（1/2））^（1/3）-2/（3·（100＋12·（69）^（1/2）））^（1/3）＋4/3≈0.2451223338. We consider connected r-uniform hypergraphs with spectral radius between ρ_r and ρ′_r and give a description of such hypergraphs.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10961007, 10871210)Natural Science Foundation of Guangxi Province (Grant No. 0991101)Guangxi Education Department
文摘A subgroup H of a finitegroup G is called a c＊-normal subgroup of G if there exists a
