ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 69,   1   (2000)
pp.   71-76

DEGREES, NEIGHBOURHOODS, AND CLOSURE OPERATIONS
L. STACHO

Abstract.  Closure theorems in graph theory are of the following type: Let $G$ be a graph, $\cal P$ a graph theoretic property, and let $u$ and $v$ be two non-adjacent vertices of $G$. If condition $c(u,v)$ holds, then $G$ has property $\cal P$ if and only if $G+uv$ has $\cal P$. We discuss several such results of the above type where the condition $c(u,v)$ refers to neighbourhood properties of $u$ and $v$.

AMS subject classification.  05C38, 05C45
Keywords