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 Arboricity Conjecture (LAC), stating that every $d$-regular graph $G$ has linear arboricity $\\lceil ...
On the Linear Arboricity of Graphs with Treewidth at Most Four Article 19 June 2023 Total coloring of 1-toroidal graphs with maximum degree at least 11 and no adjacent triangles Article 03 May 2016 References Bermond, J.C., Fouquet, J.L., Habib, M., Péroche, B.: On linear k...
On the linear k-arboricity of cubic graphsA linear forest is a forest each of whose components are paths. The linear arboricity of a graph is the minimum number of linear forests required to partition E(G) and is denoted by la(G). It is conjectured that la(G) = [(螖+1)/2] for...
In this paper we discuss a new edge-partition problem by introducing the triple arboricity of graphs. A triple arboricity, denoted ta(G), of a graphGis defined as the minimum numberksuch that the edge set ofGcan be decomposed intoksubgraphs, each being a forest of maximum degree at most...
Given a graph G, we define its linear arboricity, denoted by la(G), to be the minimum number of edge-disjoint linear forests in G whose union is E(G). This notion was introduced by Harary [16] in 1970 as one of the covering invariants of graphs, and has been studied quite ...
Note that the class of 0-bend graphs coincides with the well-known class of interval graphs, i.e., intersection graphs of intervals on a real line. Interval graphs have many nice properties, in particular they are recognizable in linear time [6]. It is thus natural to view k-bend graphs...
1) the edge lin-ear arboricity of a graph 图的边线荫度 2) the vertice linear arboricity of a graph 图的点线荫度 3) Vertex Arboricity of Square Graphs 平方图的点荫度 4) The List Point Arboricity of Graphs 图的列表点荫度 例句>>
1) the vertice linear arboricity of a graph 图的点线荫度 2) Vertex Arboricity of Square Graphs 平方图的点荫度 3) The List Point Arboricity of Graphs 图的列表点荫度 例句>> 4) the edge lin-ear arboricity of a graph 图的边线荫度
A short proof of the linear arboricity for cubic graphs Akiyama, Exoo and Harary proved in [1] that the linear arboricity for cubic graphs is 2. They did not seek a short proof of this result but derived it in order to illustrate certain proof techniques, so called "necessary subgraphs ...
On the linear vertex arboricity of graphs The linear-vertex arboricity of various classes of simple graphs are determined. In particular, the joins of various types of graphs turn out to provide nice structures that are related to their linear vertex arboricity. The ... KH Hang - 《Ph D》 ...