|
Сибирские электронные математические известия, 2010, том 7, страницы 275–283
(Mi semr244)
|
|
|
|
Эта публикация цитируется в 8 научных статьях (всего в 8 статьях)
Статьи
Acyclic 3-choosability of planar graphs with no cycles of length from 4 to 11
O. V. Borodinab, A. O. Ivanovac a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University
c Institute of Mathematics at Yakutsk State University
Аннотация:
Every planar graph is known to be acyclically 7-choosable and is conjectured to be acyclically 5-choosable (Borodin et al., 2002). This conjecture if proved would imply both Borodin's acyclic 5-color theorem (1979) and Thomassen's 5-choosability theorem (1994). However, as yet it has been verified only for several restricted classes of graphs. Some sufficient conditions are also obtained for a planar graph to be acyclically 4- and 3-choosable.
In particular, a planar graph of girth at least 7 is acyclically 3-colorable (Borodin, Kostochka and Woodall, 1999) and acyclically 3-choosable (Borodin et al., 2010). A natural measure of sparseness, introduced by Erdős and Steinberg, is the absence of k-cycles, where 4⩽k⩽C. Here, we prove that every planar graph with no cycles of length from 4 to 11 is acyclically 3-choosable.
Ключевые слова:
acyclic coloring, planar graph, forbidden cycles.
Поступила 9 августа 2010 г., опубликована 17 сентября 2010 г.
Образец цитирования:
O. V. Borodin, A. O. Ivanova, “Acyclic 3-choosability of planar graphs with no cycles of length from 4 to 11”, Сиб. электрон. матем. изв., 7 (2010), 275–283
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/semr244 https://www.mathnet.ru/rus/semr/v7/p275
|
|