Interleaved adjoints of directed graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10104489" target="_blank" >RIV/00216208:11320/11:10104489 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.ejc.2011.03.013" target="_blank" >http://dx.doi.org/10.1016/j.ejc.2011.03.013</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ejc.2011.03.013" target="_blank" >10.1016/j.ejc.2011.03.013</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Interleaved adjoints of directed graphs

Popis výsledku v původním jazyce

For an integer k }= 1, the kth interleaved adjoint of a digraph G is the digraph l(k)(G) with vertex-set V(G)(k), and arcs ((u(1), ... ,u(k)). (v(1), ... , v(k))) such that (u(i), v(i)) is an element of A(G) for i = 1, ... , k and (v(i), u(i+1)) is an element of A(G) for i = 1, ... , k - 1. For every k, we derive upper and lower bounds for the chromatic number of l(k)(G) in terms of that of G. In the case where G is a transitive tournament, the exact value of the chromatic number of l(k)(G) has been determined by [H.G. Yeh, X. Zhu, Resource-sharing system scheduling and circular chromatic number, Theoret. Comput. Sci. 332 (2005) 447-460]. We use the latter result in conjunction with categorical properties of adjoint functors to derive the following consequence. For every integer l, there exists a directed path Q(l) of algebraic length l which admits homomorphisms into every directed graph of chromatic number at least 4. We discuss a possible impact of this approach on the multifactor v

Název v anglickém jazyce

Interleaved adjoints of directed graphs

Popis výsledku anglicky

For an integer k }= 1, the kth interleaved adjoint of a digraph G is the digraph l(k)(G) with vertex-set V(G)(k), and arcs ((u(1), ... ,u(k)). (v(1), ... , v(k))) such that (u(i), v(i)) is an element of A(G) for i = 1, ... , k and (v(i), u(i+1)) is an element of A(G) for i = 1, ... , k - 1. For every k, we derive upper and lower bounds for the chromatic number of l(k)(G) in terms of that of G. In the case where G is a transitive tournament, the exact value of the chromatic number of l(k)(G) has been determined by [H.G. Yeh, X. Zhu, Resource-sharing system scheduling and circular chromatic number, Theoret. Comput. Sci. 332 (2005) 447-460]. We use the latter result in conjunction with categorical properties of adjoint functors to derive the following consequence. For every integer l, there exists a directed path Q(l) of algebraic length l which admits homomorphisms into every directed graph of chromatic number at least 4. We discuss a possible impact of this approach on the multifactor v

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/1M0545" target="_blank" >1M0545: Institut Teoretické Informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

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

Název periodika

European Journal of Combinatorics

ISSN

0195-6698

e-ISSN

—

Svazek periodika

32

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

7

Strana od-do

1018-1024

Kód UT WoS článku

000294580100006

EID výsledku v databázi Scopus

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