Decompositions of graphs into forests with bounded maximum degree
نویسندگان
چکیده
منابع مشابه
k-forested choosability of graphs with bounded maximum average degree
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...
متن کاملk-forested choosability of graphs with bounded maximum average degree
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 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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For a family F of graphs, a graph U is induced-universal for F if every graph in F is an induced subgraph of U . We give a construction for an induceduniversal graph for the family of graphs on n vertices with degree at most r, which has Cnb(r+1)/2c vertices and Dn2b(r+1)/2c−1 edges, where C and D are constants depending only on r. This construction is nearly optimal when r is even in that such...
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For a loopless multigraph G, the fractional arboricity Arb(G) is the maximum of |E(H)| |V (H)|−1 over all subgraphs H with at least two vertices. Generalizing the NashWilliams Arboricity Theorem, the Nine Dragon Tree Conjecture asserts that if Arb(G) ≤ k + d k+d+1 , then G decomposes into k + 1 forests with one having maximum degree at most d. The conjecture was previously proved for (k, d) ∈ {...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90377-e