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112
More Results on rInflated Graphs: Arboricity, Thickness, Chromatic Number, and Fractional Chromatic Number
, 2010
"... In 1890, P. J. Heawood published his famous article Mapcolour theorem in the Quarterly Journal of Mathematics [Hea90] that illustrated the flaw in A.B. Kempe’s “proof” of the Four Colour Theorem [Kem79]. Heawood’s main intention was to investigate generalizations of the Four Colour Problem “of wh ..."
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In 1890, P. J. Heawood published his famous article Mapcolour theorem in the Quarterly Journal of Mathematics [Hea90] that illustrated the flaw in A.B. Kempe’s “proof” of the Four Colour Theorem [Kem79]. Heawood’s main intention was to investigate generalizations of the Four Colour Problem “of which strangely the rigorous proof is much
THE LINEAR ARBORICITY OF GRAPHS
, 1988
"... A linear forest is a forest in which each connected component is a path. The linear arboricity la(G) of a graph G is the minimum number of linear forests whose union is the set of all edges of G. The linear arboricity conjecture asserts that for every simple graph G with maximum degree A = A(G), Alt ..."
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Cited by 61 (11 self)
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A linear forest is a forest in which each connected component is a path. The linear arboricity la(G) of a graph G is the minimum number of linear forests whose union is the set of all edges of G. The linear arboricity conjecture asserts that for every simple graph G with maximum degree A = A
Characterizations of arboricity of graphs
 Ars Combinatorica
"... The aim of this paper is to give several characterizations for the following two classes of graphs: (i) graphs for which adding any l edges produces a graph which is decomposible into k spanning trees and (ii) graphs for which adding some l edges produces a graph which is decomposible into k spannin ..."
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Cited by 17 (1 self)
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The aim of this paper is to give several characterizations for the following two classes of graphs: (i) graphs for which adding any l edges produces a graph which is decomposible into k spanning trees and (ii) graphs for which adding some l edges produces a graph which is decomposible into k
The Fractional Vertex Arboricity of Graphs
"... The vertex arboricity va(G) of a graph G is the minimum number of subsets into which the vertex set V (G) can be partitioned so that each subset induces an acyclic subgraph. The fractional version of the vertex arboricity is introduced in this paper. We determine the fractional vertex arboricity for ..."
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Cited by 1 (0 self)
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The vertex arboricity va(G) of a graph G is the minimum number of subsets into which the vertex set V (G) can be partitioned so that each subset induces an acyclic subgraph. The fractional version of the vertex arboricity is introduced in this paper. We determine the fractional vertex arboricity
Linear Arboricity and Linear kArboricity of Regular Graphs
 GRAPHS COMBIN
, 2001
"... We find upper bounds on the linear karboricity of dregular graphs using a probabilistic argument. For small k these bounds are new. For large k they blend into the known upper bounds on the linear arboricity of regular graphs. ..."
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Cited by 11 (3 self)
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We find upper bounds on the linear karboricity of dregular graphs using a probabilistic argument. For small k these bounds are new. For large k they blend into the known upper bounds on the linear arboricity of regular graphs.
Bounds on the arboricities of connected graphs
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 49 (2011), PAGES 209–215
, 2011
"... The vertex [edge] arboricity a(G) [a1(G)] of a graph G is the minimum number of subsets into which V (G) [E(G)] can be partitioned so that each subset induces an acyclic subgraph. Let G(m, n) be the class of connected simple graphs of order n and size m and let π ∈{a, a1}. In this paper we determine ..."
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The vertex [edge] arboricity a(G) [a1(G)] of a graph G is the minimum number of subsets into which V (G) [E(G)] can be partitioned so that each subset induces an acyclic subgraph. Let G(m, n) be the class of connected simple graphs of order n and size m and let π ∈{a, a1}. In this paper we
On linear arboricity of cubic graphs
, 2007
"... A linear forest is a graph in which each connected component is a chordless path. A linear partition of a graph G is a partition of its edge set into linear forests and la(G) is the minimum number of linear forests in a linear partition. When each path has length at most k a linear forest is a linea ..."
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Cited by 2 (2 self)
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A linear forest is a graph in which each connected component is a chordless path. A linear partition of a graph G is a partition of its edge set into linear forests and la(G) is the minimum number of linear forests in a linear partition. When each path has length at most k a linear forest is a
On incidence coloring and star arboricity of graphs
 Discrete Math
"... In this note we show that the concept of incidence coloring introduced in [BM] is a special case of directed star arboricity, introduced in [AA]. A conjecture in [BM] concerning asmyptotics of the incidence coloring number is solved in the negative following an example in [AA]. We generalize Theore ..."
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Cited by 9 (0 self)
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Theorem 2.1 of [AMR] concerning the star arboricity of graphs to the directed case by a slight modification of their proof, to give the same asymptotic bound as in the undirected case. As a result, we get tight asymptotic bounds for the maximum incidence coloring number of a graph in terms of its degree
On the Linear Arboricity of 1Planar Graphs∗
"... Abstract It is proved that the linear arboricity of every 1planar graph with maximum degree ∆> 33 is ⌈∆/2⌉. ..."
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Abstract It is proved that the linear arboricity of every 1planar graph with maximum degree ∆> 33 is ⌈∆/2⌉.
Results 1  10
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