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On the linear arboricity of planar graphs

โœ Scribed by Wu, Jian-Liang

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
188 KB
Volume
31
Category
Article
ISSN
0364-9024

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โœฆ Synopsis

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† =

๐Ÿ“œ SIMILAR VOLUMES

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A well-known Tutte's theorem claims that every 3-connected planar graph has a convex embedding into the plane. Tutte's arguments also show that, moreover, for every nonseparating cycle C of a 3-connected graph G, there exists a convex embedding of G such that C is a boundary of the outer face in thi

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Given a graph G, a total k-coloring of G is a simultaneous coloring of the vertices and edges of G with at most k colors. If โˆ†(G) is the maximum degree of G, then no graph has a total โˆ†-coloring, but Vizing conjectured that every graph has a total (โˆ† + 2)-coloring. This Total Coloring Conjecture rem