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Equitable coloring of corona products of cubic graphs is harder than ordinary coloringFurmańczyk, Hanna ; Kubale, Marek, 1946-Graf se imenuje nepristransko ▫$k$▫-obarvljiv, če lahko njegova vozlišča razvrstimo v ▫$k$▫ neodvisnih množic na tak način, da se število vozlišč v poljubnih dveh množicah razlikuje za največ ena. ... Najmanjši ▫$k$▫, za katerega obstaja takšno barvanje, je znan kot nepristransko kromatsko število grafa ▫$G$▫ in ga označimo ▫$\chi_=(G)$▫. V tem članku študiramo problem določitve ▫$\chi_ =$▫ za krone kubičnih grafov. Čeprav je problem navadnega barvanja kron kubičnih grafov rešljiv v polinomskem času, je problem nepristranskega barvanja za te grafe NP-težak. Prikažemo polinomsko rešljive primere kron kubičnih grafov in dokažemo NP-težavnost v splošnem primeru. Kot stranski produkt dobimo preprost algoritem z linearno časovno zahtevnostjo za nepristransko barvanje takšnih grafov, ki uporabi ▫$\chi_=(G)$▫ ali ▫$\chi_=(G)+1$▫ barv. Naš algoritem je najboljši možen, razen če P=NP. Posledično, kubični kronski grafi se zdijo edini znani razred grafov, za katere je nepristransko barvanje težje kot običajno barvanje.Source: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 10, no. 2, 2016, str. 333-347)Type of material - article, component part ; adult, seriousPublish date - 2016Language - englishCOBISS.SI-ID - 17834585
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Furmańczyk, Hanna | |
Kubale, Marek, 1946- |
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