A graph is color‐critical if it contains an edge whose removal reduces its chromatic number.
Let T n, k T_n,k be the Turán graph with nn vertices and kk parts. Given a graph HH, let ex …

The Turán number of a graph H, denoted by ex (n, H), is the maximum number of edges in a
simple graph of order n which does not contain H as a subgraph. In this paper, we determine …

Let F=∪ i= 1 k S di be the union of pairwise vertex-disjoint k stars of order d 1+ 1,…, d k+ 1,
respectively, where k≥ 2 and d 1≥⋯≥ dk≥ 1. In this paper, we present two sharp upper …

Given two graphs H and F, the maximum possible number of copies of H in an F-free graph
on n vertices is denoted by ex (n, H, F). We investigate the function ex (n, H, k F), where k F …

The Turán type extremal problems ask to maximize the number of edges over all graphs
which do not contain fixed subgraphs. Similarly, their spectral counterparts ask to maximize …

The anti-Ramsey problem was introduced by Erdös, Simonovits, and Sós in 1970s. The
anti-Ramsey number of a hypergraph H, ar (n, s, H), is the smallest integer c such that in any …

We consider $2 $-colourings $ f: E (G)\rightarrow\{-1, 1\} $ of the edges of a graph $ G $ with
colours $-1$ and $1 $ in $\mathbb {Z} $. A subgraph $ H $ of $ G $ is said to be a zero-sum …

The extremal graphs $\mathrm {EX}(n,\mathcal F) $ and spectral extremal graphs $\mathrm
{SPEX}(n,\mathcal F) $ are the sets of graphs on $ n $ vertices with maximum number of …

The Turán number of a graph H, denoted by ex (n, H), is the maximum number of edges in
any graph on n vertices containing no H as a subgraph. Let S ℓ denote the star on ℓ+ 1 …

The generalized Turán number ex (n, K s, H) is defined to be the maximum number of copies
of a complete graph K s in any H-free graph on n vertices. Let F be a linear forest consisting …