The Crossing Number of the Cone of a Graph

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F18%3A00106879" target="_blank" >RIV/00216224:14330/18:00106879 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1137/17M1115320" target="_blank" >http://dx.doi.org/10.1137/17M1115320</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/17M1115320" target="_blank" >10.1137/17M1115320</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Crossing Number of the Cone of a Graph

Popis výsledku v původním jazyce

Motivated by a problem asked by Richter and by the long standing Harary{Hill conjecture, we study the relation between the crossing number of a graph G and the crossing number of its cone CG, the graph obtained from G by adding a new vertex adjacent to all the vertices in G. Simple examples show that the di ff erence cr (CG) - cr (G) can be arbitrarily large for any fi xed k = cr (G). In this work, we are interested in fi nding the smallest possible di ff erence; that is, for each nonnegative integer k, fi nd the smallest f (k) for which there exists a graph with crossing number at least k and cone with crossing number f (k). For small values of k, we give exact values of f (k) when the problem is restricted to simple graphs and show that f (k) = k + circle minus(root k) when multiple edges are allowed.

Název v anglickém jazyce

The Crossing Number of the Cone of a Graph

Popis výsledku anglicky

Motivated by a problem asked by Richter and by the long standing Harary{Hill conjecture, we study the relation between the crossing number of a graph G and the crossing number of its cone CG, the graph obtained from G by adding a new vertex adjacent to all the vertices in G. Simple examples show that the di ff erence cr (CG) - cr (G) can be arbitrarily large for any fi xed k = cr (G). In this work, we are interested in fi nding the smallest possible di ff erence; that is, for each nonnegative integer k, fi nd the smallest f (k) for which there exists a graph with crossing number at least k and cone with crossing number f (k). For small values of k, we give exact values of f (k) when the problem is restricted to simple graphs and show that f (k) = k + circle minus(root k) when multiple edges are allowed.

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

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

—

Svazek periodika

32

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

2080-2093

Kód UT WoS článku

000450810500026

EID výsledku v databázi Scopus

2-s2.0-85053860050