On Induced Online Ramsey Number of Paths, Cycles, and Trees

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10404271" target="_blank" >RIV/00216208:11320/19:10404271 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/978-3-030-19955-5_6" target="_blank" >https://doi.org/10.1007/978-3-030-19955-5_6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-19955-5_6" target="_blank" >10.1007/978-3-030-19955-5_6</a>

Result language

angličtina

Original language name

On Induced Online Ramsey Number of Paths, Cycles, and Trees

Original language description

An online Ramsey game is a game between Builder and Painter, alternating in turns. They are given a fixed graph H and a an infinite set of independent vertices G. In each round Builder draws a new edge in G and Painter colors it either red or blue. Builder wins if after some finite round there is a monochromatic copy of the graph H, otherwise Painter wins. The online Ramsey number (r) over tilde (H) is the minimum number of rounds such that Builder can force a monochromatic copy of H in G. This is an analogy to the size-Ramsey number (r) over bar (H) defined as the minimum number such that there exists graph G with (r) over bar (H) edges where for any edge two-coloring G contains a monochromatic copy of H. In this extended abstract, we introduce the concept of induced online Ramsey numbers: the induced online Ramsey number (r) over tilde (ind)(H) is the minimum number of rounds Builder can force an induced monochromatic copy of H in G. We prove asymptotically tight bounds on the induced online Ramsey numbers of paths, cycles and two families of trees. Moreover, we provide a result analogous to Conlon [On-line Ramsey Numbers, SIAM J. Discr. Math. 2009], showing that there is an infinite family of trees T-1, T-2,..., vertical bar T-i vertical bar &lt; vertical bar Ti+1 vertical bar for i &gt;= 1, such that (i -&gt;infinity)lim &lt;(r)over tilde&gt;(T-i)/(r) over bar (T-i) = 0.

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

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

Project

—

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2019

Confidentiality

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

Article name in the collection

COMPUTER SCIENCE - THEORY AND APPLICATIONS

ISBN

978-3-030-19955-5

ISSN

0302-9743

e-ISSN

1611-3349

Number of pages

10

Pages from-to

60-69

Publisher name

SPRINGER INTERNATIONAL PUBLISHING AG

Place of publication

CHAM

Event location

Novosibirsk

Event date

Jul 1, 2019

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

000490894900006