\magnification=1200
\hsize=4in
\overfullrule=0pt
\nopagenumbers
\noindent
%
%
{\bf Yair Caro and Raphael Yuster}
%
%
\medskip
\noindent
%
%
{\bf The Order of Monochromatic Subgraphs with a Given Minimum Degree}
%
%
\vskip 5mm
\noindent
%
%
%
%
Let $G$ be a graph. For a given positive integer $d$,
let $f_G(d)$ denote the largest integer $t$ such that in every
coloring of the edges of $G$ with two colors there is a monochromatic
subgraph with minimum degree at least $d$ and order at least $t$. Let
$f_G(d)=0$ in case there is a $2$-coloring of the edges of $G$ with no
such monochromatic subgraph.  Let $f(n,k,d)$ denote the minimum of
$f_G(d)$ where $G$ ranges over all graphs with $n$ vertices and
minimum degree at least $k$.  In this paper we establish $f(n,k,d)$
whenever $k$ or $n-k$ are fixed, and $n$ is sufficiently large.  We
also consider the case where more than two colors are allowed.


\bye

.
