Bears with Hats and Independence Polynomials

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10431910" target="_blank" >RIV/00216208:11320/21:10431910 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21240/21:00355330

Result on the web

<a href="https://arxiv.org/abs/2103.07401" target="_blank" >https://arxiv.org/abs/2103.07401</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-86838-3" target="_blank" >10.1007/978-3-030-86838-3</a>

Result language

angličtina

Original language name

Bears with Hats and Independence Polynomials

Original language description

Consider the following hat guessing game. A bear sits on each vertex of a graph G, and a demon puts on each bear a hat colored by one of h colors. Each bear sees only the hat colors of his neighbors. Based on this information only, each bear has to guess g colors and he guesses correctly if his hat color is included in his guesses. The bears win if at least one bear guesses correctly for any hat arrangement. We introduce a new parameter - fractional hat chromatic number μ^, arising from the hat guessing game. The parameter μ^ is related to the hat chromatic number which has been studied before. We present a surprising connection between the hat guessing game and the independence polynomial of graphs. This connection allows us to compute the fractional hat chromatic number of chordal graphs in polynomial time, to bound fractional hat chromatic number by a function of maximum degree of G, and to compute the exact value of μ^ of cliques, paths, and cycles.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

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

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

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

Publication year

2021

Confidentiality

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

Article name in the collection

Graph-Theoretic Concepts in Computer Science

ISBN

978-3-030-86837-6

ISSN

0302-9743

e-ISSN

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Number of pages

13

Pages from-to

283-295

Publisher name

Springer, Cham

Place of publication

Neuveden

Event location

Varšava, Polsko

Event date

Jun 23, 2021

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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