2018/12/05 by Wang, Jian, Yang, Weihua
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1812.01940
Let F be a family of r-graphs. The Turán number exr(n;F) is defined to be the maximum number of edges in an r-graph of order n that is F-free. The famous Erdős Matching Conjecture shows that exr(n,Mk+1(r))= max\\binomrk+r-1r,\binomnr-\binomn-kr\, where Mk+1(r) represents the r-graph consisting of k+1 disjoint edges. Motivated by this conjecture, we consider the Turán problem for tight linear forests. A tight linear forest is an r-graph whose connected components are all tight paths or isolated vertices. Let Ln,k(r) be the family of all tight linear forests of order n with k edges in r-graphs. In this paper, we prove that for sufficiently large n, exr(n;Ln,k(r))=max\\binomkr, \binomnr-\binomn-\lfloor (k-1)/r \rfloorr\+d, where d=o(nr) and if r=3 and k=cn with 0