Linear 2-arboricity of coupled graphs
Nettet15. jul. 2014 · The linear-k-arboricity of G (denoted lak (G)) is the minimum number of linear k-forests which partition E(G). We study this new index in two cases: cubic … Nettet6. mar. 2024 · The figure shows the complete bipartite graph K 4,4, with the colors indicating a partition of its edges into three forests. K 4,4 cannot be partitioned into fewer forests, because any forest on its eight vertices has at most seven edges, while the overall graph has sixteen edges, more than double the number of edges in a single forest. . …
Linear 2-arboricity of coupled graphs
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Nettet21. mai 2024 · The linear arboricity of a graph G is the minimum number of linear forests of G covering all edges. In 1980, Akiyama, Exoo, and Harary proposed a conjecture, … NettetA fundamental question in this context is the "linear arboricity conjecture" of Aki yama, Exoo and Harary [2]. Conjecture 1 If G is an r-regular graph, then la(G) = rr;11. For non regular graphs we state a version of this conjecture formulated by A'it djafer [1]. Conjecture 2 If G is a graph, then 2. Structural Results
NettetThe linear arboricity has been determined for complete bipartite graphs [1], complete regular multi-partite graphs [20], Halin graphs [16], series-parallel graphs [18] and … Nettet1. jan. 2024 · The linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G. In this paper, it is proved that for two fixed integers i and j (3≤i≤j≤5), if a...
Nettet15. des. 2024 · The linear arboricity l a (G) of a graph G, initiated by Harary [17], is the minimum number t for which G has a t-linear coloring. The linear arboricity has been determined for complete bipartite graphs [2], complete regular multipartite graphs [32], Halin graphs [27], series–parallel graphs [30] and regular graphs with Δ = 3, 4 [3], 5, … NettetThe linear 2-arboricity of a graph G is the least number of forests which decomposes E ( G ) and each forest is a collection of paths of length at most two. A graph has property P k, if each subgraph H satisfies one of the three conditions: (i) δ ( H ) ≤ 1; (ii) there exists x y ∈ E ( H ) with deg H ( x ) + deg H ( y ) ≤ k; (iii) H contains a 2-alternating cycle.
Nettet22. jun. 1999 · 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 that $ …
Nettet1. feb. 2010 · The linear 2-arboricity, the linear 3-arboricity and a lower bound of linear k-arboricity of balanced complete bipartite graphs are obtained in [9,10,11], … fidelity in mental healthNettet13. des. 2024 · The linear arboricity of a graph $G$ is the minimum number of linear forests of $G$ covering all edges. In 1980, Akiyama, Exoo and Harary proposed a conjecture, known as the Linear... grey dinnerware with gold rimNettetThe notion of linear A:-arboricity of a graph was first introduced by Habib and Peroche [13]. It is a natural generalization of edge coloring. Clearly, a linear ... The linear 2-arboricity, the linear 3-arboricity and a lower bound of linear A:-arboricity of balanced complete bipartite graphs are obtained in [9, 10, 11], fidelity inherited ira bdaNettetThe linear 2-arboricity of a graph G is the least number of forests which decomposes E ( G ) and each forest is a collection of paths of length at most two. A graph has property … fidelity initial investment roth iragrey dining table walnut topNettet1. jan. 1994 · It is obtained that the linear 2arboricity, the linear 3-arboricity and the low bound of linear k-arboricity of balanced complete bipartite graph in [8,9, 10], … grey direct 11 w. 42nd stNettet19. des. 2024 · By applying those structural theorems, we confirm the Linear Arboricity Conjecture for NIC-planar graphs with maximum degree at least 14 and determine the … grey direct advertising