On the linear arboricity of 1-planar graphs

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August undefined, 2024

WebWe investigate the total coloring of fullerene nanodiscs, a subclass of cubic planar graphs with girth 5 arising in Chemistry, ... List strong linear 2-arboricity of sparse graphs. … Web1 de mai. de 2008 · Chartrand and Kronk [9] provided a planar graph of the vertex-arboricity 3. Poh [22] strengthened this result by showing that the linear vertex-arboricity of planar graphs is at most 3. The following theorem, which will be cited later, characterizes completely maximal plane graphs with the vertex-arboricity 2. Theorem 1 [24]

On the vertex-arboricity of planar graphs - ScienceDirect

Web, On the linear 2-arboricity of planar graphs without intersecting 3-cycles or intersecting 4-cycles, Ars Combin. 136 (2024) 383 – 389. Google Scholar [30] Zhang L., The linear 2 … Web1 de ago. de 2007 · The linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that @?@D(G) ... Wu, J.L., On the linear arboricity of planar graphs. J. Graph Theory. v31. 129-134. Google Scholar [13] Wu, J.L., The linear arboricity of series¿parallel graphs. phillip mighty med

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WebOn the linear 2-arboricity of planar graph without normally adjacent 3-cycles and 4-cycles. Yiqiao Wang School of Management, Beijing University of Chinese Medicine, Beijing, … WebActually, every outer-1-planar graph is planar. This factwasreleasedin[10]withoutdetailedproof,andaformalproofwasgivenbyAuer et al.[12]. A … Web26 de mai. de 2024 · Linear Arboricity of 1-Planar Graphs; Edge Degree Conditions for Dominating and Spanning Closed Trails; Extremal Graphs for Even Linear Forests in Bipartite Graphs; ℓ-Covering k-Hypergraphs are Quasi-Eulerian; Zero and Total Forcing Dense Graphs; The Walks and CDC of Graphs with the Same Main Eigenspace; Total … phillip miles brisbane

On the vertex-arboricity of planar graphs - ScienceDirect

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WebWe prove in this note that the linear vertex-arboricity of any planar graph is at most three, which confirms a conjecture due to Broere and Mynhardt, and others. Citing Literature. Volume 14, Issue 1. March 1990. Pages 73-75. Related; Information; Close Figure Viewer. Return to Figure. Previous Figure Next Figure. phillip millard pastorWebargues that the approximation factor of the algorithm is respectively 3.5+ε and α+2+ε for planar graphs and α-bounded arboricity graphs. As a consequence of the above lemma, we show improved bounds for the approximation factor the algorithm in [7] getting the following algorithmic corollary. Corollary 1 Let G be a planar graph of order n. phillip miller longwood university

"Web1-planar graphs G, Zhang, Liu and Wu[12] showed that if Δ(G) ≥ 33 then la(G)= Δ(G) 2. In this paper, we aim to partially solve LAC for NIC-planar graphs with large maximum degree by proving the following Theorem 1.2. If G is an NIC-planar graph with Δ(G) ≥ 14,thenla(G) ≤ Δ(G)+1 2. In addition, we prove the second theorem on the linear ... " - On the linear arboricity of 1-planar graphs

On the linear arboricity of 1-planar graphs

WebThe linear 2-arboricity la2(G) of a graph G is the least integer k such that G can be partitioned into k edge-disjoint forests, ... Zhang, G. Liu and J. Wu, On the linear arboricity of 1-planar graphs, Oper. Res. Trans. 3 (2011) 38–44. Google Scholar; 19. X. Zhang and J. Wu, On edge colorings of 1-planar graphs, Inform. WebThe linear 2-arboricity la2(G) of a graph G is the least integer k such that G can be partitioned into k edge-disjoint forests, ... Zhang, G. Liu and J. Wu, On the linear …

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Webindex ˜0(G) of a graph. The ordinary linear arboricity la(G) (or la 1(G)) is the case where every component of each forest is a path without length constraint. ur-F thermore, the linear karboricity is a re nement of the ordinary linear arboricit.y The Cartesian product of m graphs G 1;G 2; ;G m is the graph H = G 12G 22 2G m, where V(H) = Qm i ... WebWe investigate the total coloring of fullerene nanodiscs, a subclass of cubic planar graphs with girth 5 arising in Chemistry, ... List strong linear 2-arboricity of sparse graphs. 2011 • Anna Ivanova. Download Free PDF View PDF. Total colorings of graphs of order 2n having maximum degree 2n− 2. Hung-lin Fu.

WebThe linear 2-arboricity la 2(G) of G is the least integer k such that G can be partitioned into k... Let G be a planar graph with maximum degree Δ and girth g. The linear 2 … Webdedicates to the linear arboricity of graphs 1-embedded on a given surface, will be shown at the end of the paper. Theorem 2 For every 1-planar graph G with maximum degree ∆ 6 M and M > 34, we have...

WebThe linear 2-arboricity la2(G) of a graph G is the least integer k such that G can be partitioned into k edge-disjoint forests, ... Qian and W. Wang, The linear 2-arboricity of planar graphs without 4-cycles, J. Zhejiang Norm. Univ. 29 (2006) 121–125 (in Chinese). Web19 de dez. de 2024 · A graph is NIC-planar if it admits a drawing in the plane with at most one crossing per edge and such that two pairs of crossing edges share at most one …

Web6 de jan. de 2016 · The linear -arboricity of , denoted by , is the least integer such that can be edge-partitioned into linear -forests. Clearly, for any . For extremities, is the chromatic index of ; corresponds to the linear arboricity of . The linear -arboricity of a graph was first introduced by Habib and Péroche [9]. For any graph on vertices, they put ...

WebWe prove in this note that the linear vertex-arboricity of any planar graph is at most three, which confirms a conjecture due to Broere and Mynhardt, and others. Citing Literature. … phillip millar clothingWeb23 de dez. de 2011 · Abstract. The linear arboricity la ( G) 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 … phillip miller lawyer staunton vaWeb6 de jan. de 2016 · The linear -arboricity of a graph was first introduced by Habib and Péroche [9]. For any graph on vertices, they put forward the following conjecture: This … phillip miller obituaryWebOn the linear 2-arboricity of planar graph without normally adjacent 3-cycles and 4-cycles. Yiqiao Wang School of Management, Beijing University of Chinese Medicine, Beijing, China Correspondence [email protected] View further author information. Pages 981-988 Received 14 Apr 2015. phillip miller attorneyWeb1 de jul. de 2024 · The linear 2-arboricity of planar graphs. Graphs Combin., 19 (2003), pp. 241-248. CrossRef View in Scopus Google Scholar [8] Wang Y. An improved upper … phillip miller libraryWeb30 de dez. de 2009 · The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. In 1984, Akiyama et al. stated the Linear Arboricity Conjecture (LAC), that the linear arboricity of any simple graph of maximum degree $Δ$ is either $\\lceil \\tfracΔ{2} \\rceil$ or $\\lceil \\tfrac{Δ+1}{2} \\rceil$. In [J. L. … phillip miller parkWeb22 de ago. de 2007 · The linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that ⌈ Δ ( G) 2 ⌉ ≤ l a ( G) ≤ ⌈ Δ ( G) + 1 2 ⌉ for any simple graph G. In the paper, it is proved that if G is a planar graph with Δ ≥ 7 and without i -cycles for some i ∈ { 4, 5 ... tryptophan multiple sclerosis