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The star arboricity of graphs

โœ Scribed by I. Algor; N. Alon


Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
714 KB
Volume
75
Category
Article
ISSN
0012-365X

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๐Ÿ“œ SIMILAR VOLUMES


The star-arboricity of the complete regu
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A subgraph H of a graph G is called a star-subgraph if each component of H is a star. The star-arboricify of G, denoted by sa(G), is the minimum number of star-subgraphs that partition the edges of G. In this paper we show that sa(G) is [r/21 + 1 or [r/2] + 2 for the complete r-regular multipartite

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We develop a connection between vertex coloring in graphs and star arboricity which allows us to prove that every planar graph has star arboricity at most 5. This settles an open problem raised independently by Algor and Alon and by Ringel. We also show that deciding if a graph has star arboricity 2

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In this note we show that the concept of incidence coloring introduced by Brualdi and Massey [4] is a special case of directed star arboricity, introduced by Agor and Alon ['2]. A conjecture in [4] concerning asymptotics of the incidence coloring number is solved in the negative following an example

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The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. Akiyama, Exoo, and Harary conjectured for any simple graph G with maximum degree โˆ†. The conjecture has been proved to be true for graphs having โˆ† =

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W e prove that the linear arboricity of every 5-regular graph is 3. That is, the edges of any 5-regular graph are covered by three linear forests. W e also determine the linear arboricity of 6-regular graphs and 8-regular graphs. These results improve the known upper bounds for the linear arboricity

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## Abstract In this paper, we study the critical pointโ€arboricity graphs. We prove two lower bounds for the number of edges of __k__โ€critical pointโ€arboricity graphs. A theorem of Kronk is extended by proving that the pointโ€arboricity of a graph __G__ embedded on a surface __S__ with Euler genus __