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JOURNAL OF COMBINATORIAL THEORY, Series B 37, 79-91 (1984) Regular Subgraphs of Almost Regular Graphs
 

Summary: JOURNAL OF COMBINATORIAL THEORY, Series B 37, 79-91 (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 q-regular subgraph (and hence an r-regular 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 q-regular subgraph (and hence an r-regular subgraph for all r < q, r = q

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics