The Turán number of a graph $H$, $\mathrm{ex}(n,H)$, is the maximum number of edges in a graph on $n$ vertices which does not have $H$ as a subgraph. We determine the Turán number and find the unique extremal graph for forests consisting of paths when $n$ is sufficiently large. This generalizes a result of Bushaw and Kettle [Combinatorics, Probability and Computing 20:837--853, 2011]. We also determine the Turán number and extremal graphs for forests consisting of stars of arbitrary order.
@article{10_37236_3142,
author = {Hong Liu and Bernard Lidicky and Cory Palmer},
title = {On the {Tur\'an} number of forests},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {2},
doi = {10.37236/3142},
zbl = {1298.05071},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3142/}
}
TY - JOUR
AU - Hong Liu
AU - Bernard Lidicky
AU - Cory Palmer
TI - On the Turán number of forests
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/3142/
DO - 10.37236/3142
ID - 10_37236_3142
ER -
%0 Journal Article
%A Hong Liu
%A Bernard Lidicky
%A Cory Palmer
%T On the Turán number of forests
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/3142/
%R 10.37236/3142
%F 10_37236_3142
Hong Liu; Bernard Lidicky; Cory Palmer. On the Turán number of forests. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/3142
