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Properly colored subgraphs and rainbow subgraphs in edge‐colorings with local constraints
It is shown that for fixed m and d, and all sufficiently large n compared to m andd, f(m, G) = n for all graphs G with n vertices and maximum degree at most d.
Asymptotic improvement of the Gilbert-Varshamov bound on the size of binary codes
  • T. Jiang, A. Vardy
  • Computer Science
    IEEE Transactions on Information Theory
  • 18 April 2004
It is shown that, in fact, there exists a positive constant c such that A/sub 2/(n, d)/spl ges/c2/sup n//V(n,d-1)log/ sub 2/V( n, d- 1) whenever d/n/spl les/0.499.
Exact solution of the hypergraph Turán problem for k-uniform linear paths
The intensive use of the delta-system method is used to determine exk(n, Pℓ(k) exactly for all fixed ℓ ≥1, k≥4, and sufficiently large n, and describe the unique extremal family.
Hypergraph Turán numbers of linear cycles
Constrained Ramsey numbers of graphs
Using constructions from design theory, the exact values, lying near (s 1) (t 1), are established for f (S,T ) when S and T are certain paths or star-like trees.
Turán Numbers of Subdivided Graphs
It is proved that the Turan number ex(n,H^{(p)})=O(n^{1+(16/p)}, which is the maximum number of edges in an $n$-vertex simple graph that does not contain $F$ as a subgraph.
Edge-Colorings with No Large Polychromatic Stars
  • T. Jiang
  • Mathematics
    Graphs Comb.
  • 1 May 2002
For all positive integers n and r, fr(Kn,n) exactly and fr( Kn) within 1 is determined, disproving a conjecture by Manoussakis, Spyratos, Tuza and Voigt about the largest number of colors that can be used in a coloring of E(G).