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. 2011 • Anna Ivanova. Download Free PDF View PDF. Total colorings of graphs of order 2n having maximum degree 2n− 2. Hung-lin Fu. Web30 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. …

On the linear vertex‐arboricity of a planar graph - Poh - 1990 ...

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. … Web6 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 … port of south louisiana location

A Hall-type theorem with algorithmic consequences in planar graphs

Web22 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 ... WebThe linear arboricity has been determined for complete bipartite graphs [1], complete regular multi-partite graphs [20], Halin graphs [16], series-parallel graphs [18] and regular graphs with = 3;4[2] and 5,6,8[9]. For planar graphs, more results are obtained. Conjecture A has already been proved to be true for all planar graphs (see [17] and ... Web24 de mar. de 2024 · Given a graph G, the arboricity Upsilon(G) is the minimum number of edge-disjoint acyclic subgraphs (i.e., spanning forests) whose union is G. An acyclic graph therefore has Upsilon(G)=1. It appears that a regular graph G of vertex degree d has arboricity Upsilon(G)= _n/2_ +1. (1) Let G be a nonempty graph on n vertices and m … iron kingdoms character sheet

On the linear arboricity of planar graphs - Wu - 1999 - Journal of ...

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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, China Correspondence [email protected] View further author information. Pages 981-988 Received 14 Apr 2015. 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] port of south whidbey commissioner payWebindex ˜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 ... iron kissed patricia briggs

"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... " - On the linear arboricity of 1-planar graphs

On the linear arboricity of 1-planar graphs

On the linear vertex‐arboricity of a planar graph - Poh - 1990 ...

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, … 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, then la (G) = ⌈ Δ (G) 2 ⌉. Combining Eulerʼs formula with the linear arboricity. Constructing some new structures of the planar graphs.

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http://www.iaeng.org/IJAM/issues_v48/issue_3/IJAM_48_3_17.pdf Web8 de abr. de 2024 · For planar graphs, Cygan et al. [ 6] conjectured that it is NP-complete to determine whether a given planar graph with maximum degree 4 has linear …

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. 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-arboricity of 1-planar graphs, Master’s thesis, Zhejiang Normal University, 2024. Google Scholar [31] Zhang L., Liu J.

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":"2024-04-04T13:57:19Z","timestamp ...

WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): 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 if G is a planar graph with ∆(G) ≥ 5 and without 4-cycles, then la(G) = ⌈ ∆(G) 2 ⌉. Moreover, the bound that ∆(G) ≥ 5 is sharp.

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 … iron kitchen countertopsWeb19 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 … iron kitchen cartWeb1 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 … port of south louisiana tariffWeb14 de jul. de 2024 · Clearly, for a graph with maximum degree . On the other hand, the Linear Arboricity Conjecture due to Akiyama, Exoo, and Harary from 1981 asserts that for every graph . This conjecture has been verified for planar graphs and graphs whose maximum degree is at most , or is equal to or . Given a positive integer , a graph is … iron kitchen chairsWebThe linear arboricity of a graph G is clearly the smallest integer k such that it has a k-linear coloring and is denoted by χ′ l(G). The parameter χ′ l(G) was introduced by Harary [16]. The linear arboricity conjecture, ﬁrst stated by Akiyama, Exoo and Harary [1], is as follows. Conjecture 1 (Linear Arboricity Conjecture) For every ... port of south whidbeyWebThe 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). port of south whidbey commissionersWebIt is shown in this paper that the linear arboricity of every outer-1-planar graph with maximum degree 4 is exactly 2 provided that it admits an outer-1-planar drawing … iron knee carpet instalation