1Facultad de Ciencias Físicas y Matemáticas Universidad de Chile, Santiago, Chile
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 457-462
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Guido Besomi; Matías Pavez-Signé; Maya Stein; Guido Besomi; Matías Pavez-Signé; Maya Stein. Embedding trees with maximum and minimum degree conditions. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 457-462. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a15/
@article{AMUC_2019_88_3_a15,
author = {Guido Besomi and Mat{\'\i}as Pavez-Sign\'e and Maya Stein and Guido Besomi and Mat{\'\i}as Pavez-Sign\'e and Maya Stein},
title = { Embedding trees with maximum and minimum degree conditions},
journal = {Acta mathematica Universitatis Comenianae},
pages = {457--462},
year = {2019},
volume = {88},
number = {3},
url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a15/}
}
TY - JOUR
AU - Guido Besomi
AU - Matías Pavez-Signé
AU - Maya Stein
AU - Guido Besomi
AU - Matías Pavez-Signé
AU - Maya Stein
TI - Embedding trees with maximum and minimum degree conditions
JO - Acta mathematica Universitatis Comenianae
PY - 2019
SP - 457
EP - 462
VL - 88
IS - 3
UR - http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a15/
ID - AMUC_2019_88_3_a15
ER -
%0 Journal Article
%A Guido Besomi
%A Matías Pavez-Signé
%A Maya Stein
%A Guido Besomi
%A Matías Pavez-Signé
%A Maya Stein
%T Embedding trees with maximum and minimum degree conditions
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 457-462
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a15/
%F AMUC_2019_88_3_a15
We propose the following conjecture: For every fixed $\alpha\in [0,\frac 12]$, each graph of minimum degree at least $(1+\alpha)\frac k2$ and maximum degree at least $2(1-\alpha)k$ contains each tree with $k$ edges as a subgraph. \\ Our main result is an approximate version of the conjecture for bounded degree trees and large dense host graphs. We also show that our conjecture is asymptotically best possible, which disproves a conjecture from~\cite{rohzon}.
