 
Summary: JOURNAL OF COMBINATORIAL THEORY, Series B 37, 7991 (1984)
Regular Subgraphs of Almost Regular Graphs
N. ALON*
Department of Mathematics, Massachusetts Institute of Technology,
Cambridge, Massachusetts
S. FRIEDLAND
Institute of Mathematics, Hebrew University of Jerusalem,
Jerusalem, Israel
AND
G. KALAI*
Department of Mathematics, Massachusetts Institute of Technology,
Cambridge, Massachusetts
Communicated by the Managing Editors
Received July 25, 1983
Suppose every vertex of a graph G has degree k or k + 1 and at least one vertex
has degree k + 1. It is shown that if k > 2q  2 and q is a prime power then G
contains a qregular subgraph (and hence an rregular subgraph for all r < q. r = q
(mod 2)). It is also proved that every simple graph with maximal degree A > 2q  2
and average degree d > ((2q  2)/(2q  l))(A + 1), where q is a prime power,
contains a qregular subgraph (and hence an rregular subgraph for all r < q, r = q
