The study of how the intrinsic structure of graphs ensures certain types of properties (e.g., clique-formation and graph colorings) under appropriate conditions.
Extremal Graph Theory
See also
Erdős-Stone Theorem, Extremal Graph, Ramsey Theory, Structural Ramsey Theory, Szemerédi's Regularity Lemma, Turán Graph, Turán's TheoremExplore with Wolfram|Alpha
References
Bollobás, B. Extremal Graph Theory. New York: Academic Press, 1978.Bollobás, B. Extremal Graph Theory with Emphasis on Probabilistic Methods. Providence, RI: Amer. Math. Soc., 1986.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 143, 1990.Referenced on Wolfram|Alpha
Extremal Graph TheoryCite this as:
Weisstein, Eric W. "Extremal Graph Theory." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ExtremalGraphTheory.html