On linear k-arboricity

Abstract

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Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph

“…For C ≥ 5 we can easily prove that M (C, 3) = 2, making use of a conjecture made by Bermond et al in 1984 [5] and proved by Thomassen in 1999 [19]: A linear k-forest is a forest consisting of paths of length at most k. The linear k-arboricity of a graph G is the minimum number of linear k-forests required to partition E(G), and is denoted by la k (G) [5]. Theorem 2 is equivalent to saying that, if G is cubic, then la 5 (G) = 2.…”

Placing Regenerators in Optical Networks to Satisfy Multiple Sets of Requests

“…In fact, solving a conjecture of Bermond et al [20], Thomassen proved [21] a stronger result: the edges of any cubic graph can be two-colored such that each monochromatic connected component is a path of length at most 5 (see Fig. 2(a) for an example).…”

The Linear 2-Arboricity of Planar Graphs Without Adjacent Short Cycles

“…Chang [3] and Chang et al [4] investigated the algorithmic aspects of the linear k-arboricity. It was further studied by Bermond et al [2], Jackson and Wormald [8], and Aldred and Wormald [1]. Lih, Tong and Wang [9] proved that for a planar graph G, la 2 …”

“…It was further studied by Bermond et al [2], Jackson and Wormald [8], and Aldred and Wormald [1]. Lih, Tong and Wang [9] proved that for a planar graph G, la 2 …”

“…Ma, Wu and Yu [10] proved that for a planar graph G without 5-or 6-cycles, la 2 (G) ≤ ⌈ ∆+1 2 ⌉ + 6. For a planar graph G, we will prove that (1) la 2 …”