A simple proof of Grunbaum's theorem on the 3-colourability of planar graphs having at most three 3-cycles is given, which does not employ the colouring extension.
机构:
Institute of Mathematics, Siberian Br. of Russ. Acad. of Sci., Novosibirsk 630090, RussiaInstitute of Mathematics, Siberian Br. of Russ. Acad. of Sci., Novosibirsk 630090, Russia
机构:
Chinese Acad Sci, Grad Univ, Sch Math Sci, Beijing 100049, Peoples R ChinaChinese Acad Sci, Grad Univ, Sch Math Sci, Beijing 100049, Peoples R China