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Replication in critical graphs and the persistence of monomial idealsKaiser, Tomáš ; Stehlík, Matěj ; Škrekovski, RisteMotivirani s vprašanji o monomskih idealih brez kvadratov v kolobarju polinomov so C. A. Francisco et al. [Discrete Math. 310, No. 15--16, 2176--2182 (2010)] postavili domnevo, da za vsako pozitivno ... število ▫$k$▫ in za vsak ▫$k$▫-kritičen (t.j., kritično 5-obarvljiv) graf obstaja množica vozlišč, ki ob replikaciji le-teh porodijo ▫$(k+1)$▫-kritičen graf. Hipotezo smo ovrgli ter našli neskončno družino protiprimerov. Nadalje, najmanjši član omenjene družine odgovori na vprašanje Herzoga in Hibija o funkciji globine monomskih idealih brez kvadratov v kolobarju polinomov, kot tudi na povezano vprašanje persistenčne lastnosti takšnih idealov.Source: Journal of combinatorial theory. Series A. - ISSN 0097-3165 (Vol. 123, iss. 1, 2014, str. 239-251)Type of material - article, component part ; adult, seriousPublish date - 2014Language - englishCOBISS.SI-ID - 16920665
Author
Kaiser, Tomáš |
Stehlík, Matěj |
Škrekovski, Riste
Topics
matematika |
teorija grafov |
kritični grafi |
replikacija |
pokritje ideala |
monomski ideal brez kvadratov |
persistenčna lastnost |
mathematics |
graph theory |
critical graph |
replication |
cover ideal |
square-free monomial ideal |
associated prime |
persistence property
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Database name | Field | Year |
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Kaiser, Tomáš | ![]() |
Stehlík, Matěj | ![]() |
Škrekovski, Riste | 15518 |
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