Graphs of low average degree without independent transversals
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F23%3A43966771" target="_blank" >RIV/49777513:23520/23:43966771 - isvavai.cz</a>
Result on the web
<a href="https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.22876" target="_blank" >https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.22876</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.22876" target="_blank" >10.1002/jgt.22876</a>
Alternative languages
Result language
angličtina
Original language name
Graphs of low average degree without independent transversals
Original language description
An independent transversal of a graph G with a vertex partition P is an independent set of G intersecting each block of P in a single vertex. Wanless and Wood proved that if each block of P has size at least t and the average degree of vertices in each block is at most t/4, then an independent transversal of P exists. We present a construction showing that this result is optimal: for any ε>0 and sufficiently large t, there is a family of forests with vertex partitions whose block size is at least t, average degree of vertices in each block is at most (1/4+ε)t, and there is no independent transversal. This unexpectedly shows that methods related to entropy compression such as the Rosenfeld-Wanless-Wood scheme or the Local Cut Lemma are tight for this problem. Further constructions are given for variants of the problem, including the hypergraph version.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA20-09525S" target="_blank" >GA20-09525S: Structural properties of graph classes characterized by forbidden subgraphs</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Graph Theory
ISSN
0364-9024
e-ISSN
1097-0118
Volume of the periodical
102
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
374-387
UT code for WoS article
000841136400001
EID of the result in the Scopus database
2-s2.0-85135964681