A k-edge coloring of a hypergraph H is a coloring of the edges of H with k colors such that any two intersecting edges receive distinct colors. The Erdos-Faber-Lovasz conjecture states that every loopless linear hyper...A k-edge coloring of a hypergraph H is a coloring of the edges of H with k colors such that any two intersecting edges receive distinct colors. The Erdos-Faber-Lovasz conjecture states that every loopless linear hypergraph with n vertices has an n-edge coloring. In 2021,Kang, Kelly, K¨uhn, Methuku and Osthus confirmed the conjecture for sufficiently large n. In this paper, the conjecture is verified for collision-weak hypergraphs. This result strictly extends two related ones of Bretto, Faisant and Hennecart in 2020.展开更多
We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph G<sup>k</sup>. For the k-uniform hypergraph G<sup>k</sup> underlying a non-complete graph G =...We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph G<sup>k</sup>. For the k-uniform hypergraph G<sup>k</sup> underlying a non-complete graph G = (V, E), its rupture degree r(G<sup>k</sup>) is defined as r(G<sup>k</sup>) = max{ω(G<sup>k</sup> - X) - |X| - m(G<sup>k</sup> - X): X <span style="white-space:nowrap;">⊂ V(G<sup>k</sup>), ω(G<sup>k</sup> - X) > 1}, where X is a cut set (or destruction strategy) of G<sup>k</sup>, ω(G<sup>k</sup> - X) and m(G<sup>k</sup> - X) denote the number of components and the order of a largest component in G<sup>k</sup> - X, respectively. It is shown that this parameter can be used to measure the vulnerability of networks. In this paper, the rupture degrees of several specific classes of k-uniform hypergraph are determined.展开更多
Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to cert...Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to certain conditions.This paper is to generalize the coprime labelings of graph to hypergraph.We give the definition of coprime labelings of hypergraph.By using Rosser-Schoenfeld's inequality and the coprime mapping theorem of Pomerance and Selfridge,we prove that some linear hypergraphs are prime.展开更多
An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is ...An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is denoted by . Erdös, Faber and Lovász proposed a famous conjecture that holds for any loopless linear hypergraph H with n vertices. In this paper, we show that is true for gap-restricted hypergraphs. Our result extends a result of Alesandroni in 2021.展开更多
The explicit formula for (k+l)-uniform linear acyclic hypergraphs and the counting series for unlabeled (k +1)-uniform linear acyclic hypergraphs are obtained.
The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph.It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph,a...The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph.It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph,and the unique linear unicyclic hypergraph with the largest spectral radius is a power hypergraph.In this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius,where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 12071265)the Natural Science Foundation of Shandong Province (Grant No. ZR2019MA032)。
文摘A k-edge coloring of a hypergraph H is a coloring of the edges of H with k colors such that any two intersecting edges receive distinct colors. The Erdos-Faber-Lovasz conjecture states that every loopless linear hypergraph with n vertices has an n-edge coloring. In 2021,Kang, Kelly, K¨uhn, Methuku and Osthus confirmed the conjecture for sufficiently large n. In this paper, the conjecture is verified for collision-weak hypergraphs. This result strictly extends two related ones of Bretto, Faisant and Hennecart in 2020.
文摘We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph G<sup>k</sup>. For the k-uniform hypergraph G<sup>k</sup> underlying a non-complete graph G = (V, E), its rupture degree r(G<sup>k</sup>) is defined as r(G<sup>k</sup>) = max{ω(G<sup>k</sup> - X) - |X| - m(G<sup>k</sup> - X): X <span style="white-space:nowrap;">⊂ V(G<sup>k</sup>), ω(G<sup>k</sup> - X) > 1}, where X is a cut set (or destruction strategy) of G<sup>k</sup>, ω(G<sup>k</sup> - X) and m(G<sup>k</sup> - X) denote the number of components and the order of a largest component in G<sup>k</sup> - X, respectively. It is shown that this parameter can be used to measure the vulnerability of networks. In this paper, the rupture degrees of several specific classes of k-uniform hypergraph are determined.
基金Supported by the Natural Science Foundation of Chongqing(CSTB2022NSCQ-MSX0884)。
文摘Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to certain conditions.This paper is to generalize the coprime labelings of graph to hypergraph.We give the definition of coprime labelings of hypergraph.By using Rosser-Schoenfeld's inequality and the coprime mapping theorem of Pomerance and Selfridge,we prove that some linear hypergraphs are prime.
文摘An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is denoted by . Erdös, Faber and Lovász proposed a famous conjecture that holds for any loopless linear hypergraph H with n vertices. In this paper, we show that is true for gap-restricted hypergraphs. Our result extends a result of Alesandroni in 2021.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19771040)and the Natural Science Foundation of Guangdong Province.
文摘The explicit formula for (k+l)-uniform linear acyclic hypergraphs and the counting series for unlabeled (k +1)-uniform linear acyclic hypergraphs are obtained.
基金Natural Science Foundation of China(Grant Nos.11871073,11871077)NSF of Department of Education of Anhui Province(Grant No.KJ2017A362)。
文摘The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph.It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph,and the unique linear unicyclic hypergraph with the largest spectral radius is a power hypergraph.In this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius,where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph.
