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For a graph $H$ and a $k$-chromatic graph $F,$ if the Turan graph $T_{k-1}(n)$ has the maximum number of copies of $H$ among all $n$-vertex $F$-free graphs (for $n$ large enough), then $H$ is called $F$-Turan-good, or $k$-Turan-good for short if $F$ is $K_k.$ In this paper, we construct some new classes of $k$-Turan-good graphs and prove that $P_4$ and $P_5$ are $k$-Turan-good for $kge4.$
A graph $G$ is $k$-vertex-critical if $G$ has chromatic number $k$ but every proper induced subgraph of $G$ has chromatic number less than $k$. The study of $k$-vertex-critical graphs for graph classes is an important topic in algorithmic graph theor
Given a graph $H$ and a positive integer $n,$ the Tur{a}n number of $H$ for the order $n,$ denoted ${rm ex}(n,H),$ is the maximum size of a simple graph of order $n$ not containing $H$ as a subgraph. The book with $p$ pages, denoted $B_p$, is the gra
Given a proper edge coloring $varphi$ of a graph $G$, we define the palette $S_{G}(v,varphi)$ of a vertex $v in V(G)$ as the set of all colors appearing on edges incident with $v$. The palette index $check s(G)$ of $G$ is the minimum number of distin
A proper edge coloring of a graph $G$ with colors $1,2,dots,t$ is called a emph{cyclic interval $t$-coloring} if for each vertex $v$ of $G$ the edges incident to $v$ are colored by consecutive colors, under the condition that color $1$ is considered
We consider finite simple graphs. Given a graph $H$ and a positive integer $n,$ the Tur{a}n number of $H$ for the order $n,$ denoted ${rm ex}(n,H),$ is the maximum size of a graph of order $n$ not containing $H$ as a subgraph. ErdH{o}s posed the foll