ﻻ يوجد ملخص باللغة العربية
For all integers $k,d$ such that $k geq 3$ and $k/2leq d leq k-1$, let $n$ be a sufficiently large integer {rm(}which may not be divisible by $k${rm)} and let $sle lfloor n/krfloor-1$. We show that if $H$ is a $k$-uniform hypergraph on $n$ vertices with $delta_{d}(H)>binom{n-d}{k-d}-binom{n-d-s+1}{k-d}$, then $H$ contains a matching of size $s$. This improves a recent result of Lu, Yu, and Yuan and also answers a question of Kuhn, Osthus, and Townsend. In many cases, our result can be strengthened to $sleq lfloor n/krfloor$, which then covers the entire possible range of $s$. On the other hand, there are examples showing that the result does not hold for certain $n, k, d$ and $s= lfloor n/krfloor$.
Determine the size of $r$-graphs with given graph parameters is an interesting problem. Chvatal and Hanson (JCTB, 1976) gave a tight upper bound of the size of 2-graphs with restricted maximum degree and matching number; Khare (DM, 2014) studied the
For $ngeq 3$, let $r=r(n)geq 3$ be an integer. A hypergraph is $r$-uniform if each edge is a set of $r$ vertices, and is said to be linear if two edges intersect in at most one vertex. In this paper, the number of linear $r$-uniform hypergraphs on $n
Gutman and Wagner proposed the concept of matching energy (ME) and pointed out that the chemical applications of ME go back to the 1970s. Let $G$ be a simple graph of order $n$ and $mu_1,mu_2,ldots,mu_n$ be the roots of its matching polynomial. The m
Let $mathscr{G}_{n,beta}$ be the set of graphs of order $n$ with given matching number $beta$. Let $D(G)$ be the diagonal matrix of the degrees of the graph $G$ and $A(G)$ be the adjacency matrix of the graph $G$. The largest eigenvalue of the nonneg
A connected graph $G$ is a cactus if any two of its cycles have at most one common vertex. Let $ell_n^m$ be the set of cacti on $n$ vertices with matching number $m.$ S.C. Li and M.J. Zhang determined the unique graph with the maximum signless Laplac