In this paper, we investigate the Cartesian product with respect to the strong equitable vertex k-arboricity, and demonstrate the usefulness of the proposed constructions by applying them to some instances of product networks.
In this paper, we investigate the Cartesian product with respect to the strong equitable vertex [Formula: see text]-arboricity, and demonstrate the usefulness ...
In this paper, we investigate the Cartesian product with respect to the strong equitable vertex k k -arboricity, and demonstrate the usefulness of the proposed ...
Strong Equitable Vertex Arboricity in Cartesian Product Networks is called a t-tree-coloring for short. An equitable (t, k)-tree-coloring is a (t, k)-tree ... Strong Equitable Vertex Arboricity in Cartesian Product Networks induced by each color class of the coloring is either an union of isolated vertices or.
Jun 2, 2021 · Abstract. Equitable list arboricity, introduced by Zhang in 2016, generalizes the notion of eq- uitable list coloring by requiring the subgraph induced by each color class to be acyclic. (instead of edgeless) in addition to the usual upper bound on the size of each color class.
Aug 19, 2021 · Its easily showen that for any orientation given on E, the arboricity will be smaller or equal to the maximal outgoing degree. So the arboricoty is smaller or equal to the maximal degree, in the undirected scenario. But are there no tighter bounds? Or inequalities?
Equitable improper choosability of graphs - ScienceDirect
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Dec 6, 2020 · This conjecture is strong as it implies the Hajnal-Szemerédi theorem on equitable coloring, the equitable list coloring conjecture (Kostochka, Pelsmajer, and West, 2003), the equitable vertex arboricity conjecture (Wu, Zhang, and Li, 2013), and the equitable list vertex arboricity conjecture (Zhang, ...
Throughout this paper, all graphs considered are finite and simple. Let V ( G ) and E ( G ) denote the vertex set and edge set of a graph G respectively. Let K n 1 , … , n k be a complete k-partite graph in which partite set X i has size n i for 1 ≤ i ≤ k .
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In this paper, we give some bounds and the exact values in special cases for ψk of the Cartesian, and lexicographic products of some graphs. Key–Words: Vertex cover; k-path vertex cover; Cartesian product; lexicographic product ... studied the equitable colorings of Cartesian prod- uct graphs of wheels with complete ...
The equitable vertex k-arboricity of a graph G, denoted by va = k (G), is the minimum number of induced forests into which G can be equitably partitioned, where the maximum degree of each induced forest is at most k. ... ... Note that va = k (G) and va ≡ k (G) may vary greatly.