0557945 - ÚI 2023 RIV US eng J - Journal Article
Šileikis, Matas - Warnke, L.
Counting Extensions Revisited.
Random Structures and Algorithms. Roč. 61, č. 1 (2022), s. 3-30. ISSN 1042-9832. E-ISSN 1098-2418
R&D Projects: GA ČR(CZ) GA19-08740S; GA ČR(CZ) GJ20-27757Y
Institutional support: RVO:67985807
Keywords : extreme values * random graph * rooted subgraphs * subgraphcounts
OECD category: Pure mathematics
Impact factor: 1, year: 2022 ; AIS: 1.149, rok: 2022
Method of publishing: Limited access
Result website:
http://dx.doi.org/10.1002/rsa.21050DOI: https://doi.org/10.1002/rsa.21050

We consider rooted subgraphs in random graphs, that is, extension counts such as (i) the number of triangles containing a given vertex or (ii) the number of paths of length three connecting two given vertices. In 1989, Spencer gave sufficient conditions for the event that, with high probability, these extension counts are asymptotically equal for all choices of the root vertices. For the important strictly balanced case, Spencer also raised the fundamental question as to whether these conditions are necessary. We answer this question by a careful second moment argument, and discuss some intriguing problems that remain open.
Permanent Link: http://hdl.handle.net/11104/0331829