TY - JOUR
T1 - Smaller subgraphs of minimum degree k
AU - Mousset, Frank
AU - Noever, Andreas
AU - Škorić, Nemanja
N1 - Publisher Copyright:
© 2017, Australian National University. All rights reserved.
PY - 2017/10/6
Y1 - 2017/10/6
N2 - In 1990, Erdős, Faudree, Rousseau and Schelp proved that for k ≥ 2 every graph with n ≥ k+1 vertices and (formula presented) edges contains a subgraph of minimum degree k on at most (formula presented) vertices. They conjectured that it is possible to remove at least εkn many vertices and remain with a subgraph of minimum degree k, for some εk > 0. We make progress towards their conjecture by showing that one can remove at least Ω(n/log n) many vertices.
AB - In 1990, Erdős, Faudree, Rousseau and Schelp proved that for k ≥ 2 every graph with n ≥ k+1 vertices and (formula presented) edges contains a subgraph of minimum degree k on at most (formula presented) vertices. They conjectured that it is possible to remove at least εkn many vertices and remain with a subgraph of minimum degree k, for some εk > 0. We make progress towards their conjecture by showing that one can remove at least Ω(n/log n) many vertices.
UR - http://www.scopus.com/inward/record.url?scp=85031110515&partnerID=8YFLogxK
U2 - 10.37236/7167
DO - 10.37236/7167
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AN - SCOPUS:85031110515
SN - 1079-6061
VL - 24
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 4
M1 - #P4.9
ER -