Covering planar graphs with forests, one having bounded maximum degree
نویسندگان
چکیده
منابع مشابه
Covering planar graphs with degree bounded forests
We prove that every planar graphs has an edge partition into three forests, one having maximum degree 4. This answers a conjecture of Balogh et al. (J. Combin. Theory B. 94 (2005) 147-158).We also prove that every planar graphs with girth g ≥ 6 (resp. g ≥ 7) has an edge partition into two forests, one having maximum degree 4 (resp. 2).
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A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...
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We study the problem of covering graphs with trees and a graph of bounded maximum degree. By a classical theorem of Nash-Williams, every planar graph can be covered by three trees. We show that every planar graph can be covered by two trees and a forest, and the maximum degree of the forest is at most 8. Stronger results are obtained for some special classes of planar graphs.
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a proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. a graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $g$ such that each vertex receives a color from its own list. in this paper, we prov...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2009
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2008.07.004