On the linear arboricity of 1-planar graphs
WebHá 2 dias · In particular, since the arboricity of planar graphs is b ounded by 3, setting α = 3, this estimator gives a 24 factor approximation of the matc hing size in planar graphs. In this paper, as another 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).
On the linear arboricity of 1-planar graphs
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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 ... Web1 de dez. de 2024 · The linear 2-arboricity la 2 (G) of a graph G is the least integer k such that G can be partitioned into k edge-disjoint forests, whose component trees are paths …
Webargues 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. Web22 de jun. de 1999 · Abstract The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. Akiyama, ... On the linear …
Web{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,4]],"date-time":"2024-04 … Web31 de out. de 2012 · Generalizing Tanʼs results (Tan et al., 2011 [10]) and prove that if G is a planar graph with Δ (G) ⩾ 5 and without intersecting 4-cycles and intersecting 5-cycles, …
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Web1 de jun. de 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 … something you wear that starts with yWeb30 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. … something you wear that starts with oWebAbstract We 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. Skip to … small coldwater fish ukWebActually, every outer-1-planar graph is planar. This factwasreleasedin[10]withoutdetailedproof,andaformalproofwasgivenbyAuer et al.[12]. A … something you wind upWeb6 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 ... something you wear that starts with zWeb1 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] small coleslaw kfc caloriesWeb1 de jan. de 1988 · I uzl 1. Introduction Chartrand [l] studied the point-arboricity of planar graphs and showed that the point-arboricity of a planar graph does not exceed 3. Now … something you would do in the snow