Bears with Hats and Independence Polynomials
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00372252" target="_blank" >RIV/68407700:21240/23:00372252 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.46298/DMTCS.10802" target="_blank" >https://doi.org/10.46298/DMTCS.10802</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.46298/DMTCS.10802" target="_blank" >10.46298/DMTCS.10802</a>
Alternative languages
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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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
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)
Result continuities
Project
<a href="/en/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Research Center for Informatics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete Mathematics and Theoretical Computer Science
ISSN
1462-7264
e-ISSN
1365-8050
Volume of the periodical
25
Issue of the periodical within the volume
2
Country of publishing house
FR - FRANCE
Number of pages
21
Pages from-to
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UT code for WoS article
001151132000004
EID of the result in the Scopus database
2-s2.0-85177566832