RANDOM 2-CELL EMBEDDINGS OF MULTISTARS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10453968" target="_blank" >RIV/00216208:11320/22:10453968 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=c.4w0vq8Om" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=c.4w0vq8Om</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/proc/15899" target="_blank" >10.1090/proc/15899</a>

Jazyk výsledku

angličtina

Název v původním jazyce

RANDOM 2-CELL EMBEDDINGS OF MULTISTARS

Popis výsledku v původním jazyce

Random 2-cell embeddings of a given graph G are obtained by choosing a random local rotation around every vertex. We analyze the expected number of faces, E[FG], of such an embedding which is equivalent to studying its average genus. So far, tight results are known for two families called monopoles and dipoles. We extend the dipole result to a more general family called multistars, i.e., loopless multigraphs in which there is a vertex incident with all the edges. In particular, we show that the expected number of faces of every multistar with n nonleaf edges lies in an interval of length 2/(n + 1) centered at the expected number of faces of an n-edge dipole. This allows us to derive bounds on E[FG] for any given graph G in terms of vertex degrees. We conjecture that E[FG] &lt;=O(n) for any simple n-vertex graph G.

Název v anglickém jazyce

RANDOM 2-CELL EMBEDDINGS OF MULTISTARS

Popis výsledku anglicky

Random 2-cell embeddings of a given graph G are obtained by choosing a random local rotation around every vertex. We analyze the expected number of faces, E[FG], of such an embedding which is equivalent to studying its average genus. So far, tight results are known for two families called monopoles and dipoles. We extend the dipole result to a more general family called multistars, i.e., loopless multigraphs in which there is a vertex incident with all the edges. In particular, we show that the expected number of faces of every multistar with n nonleaf edges lies in an interval of length 2/(n + 1) centered at the expected number of faces of an n-edge dipole. This allows us to derive bounds on E[FG] for any given graph G in terms of vertex degrees. We conjecture that E[FG] &lt;=O(n) for any simple n-vertex graph G.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA19-21082S" target="_blank" >GA19-21082S: Grafy a jejich algebraické vlastnosti</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Proceedings of the American Mathematical Society

ISSN

0002-9939

e-ISSN

1088-6826

Svazek periodika

150

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

3699-3713

Kód UT WoS článku

000808522600001

EID výsledku v databázi Scopus

2-s2.0-85133308483