Χ-bounded

In graph theory, a ${\displaystyle \chi }$-bounded family ${\displaystyle {\mathcal {F}}}$ of graphs is one for which there is some function ${\displaystyle f}$ such that, for every integer ${\displaystyle t}$ the graphs in ${\displaystyle {\mathcal {F}}}$ with ${\displaystyle t=\omega (G)}$ (clique number) can be colored with at most ${\displaystyle f(t)}$ colors. The function ${\displaystyle f(t)}$ is called a ${\displaystyle \chi }$-binding function for ${\displaystyle {\mathcal {F}}}$. These concepts and their notations were formulated by András Gyárfás. The use of the Greek letter chi in the term ${\displaystyle \chi }$-bounded is based on the fact that the chromatic number of a graph ${\displaystyle G}$ is commonly denoted ${\displaystyle \chi (G)}$. An overview of the area can be found in a survey of Alex Scott and Paul Seymour.