Pseudoachromatic and connected-pseudoachromatic indices of the complete graph
نویسندگان
چکیده
منابع مشابه
Connected pseudoachromatic index of complete graphs
A connected pseudocomplete n-coloring of a graph G is a (non-proper) n-coloring of the vertices of G such that each color class induces a connected subgraph and for each pair of color classes there is an edge with one end of each color; this can be viewed as a kind of “inverse image” of a clique minor. The connected pseudoachromatic index of a graph G is the largest n for which the line graph o...
متن کاملGeometric Achromatic and Pseudoachromatic Indices
The pseudoachromatic index of a graph is the maximum number of colors that can be assigned to its edges, such that each pair of different colors is incident to a common vertex. If for each vertex its incident edges have different color, then this maximum is known as achromatic index. Both indices have been widely studied. A geometric graph is a graph drawn in the plane such that its vertices ar...
متن کاملOn the Pseudoachromatic Index of the Complete Graph III
Let q = 2 be, for some β ∈ IN, and let n = q + q + 1. By exhibiting a complete colouring of the edges of Kn, we show that the pseudoachromatic number of the complete line graph Gn = L(Kn) is at least ψ(Gn) ≥ q+q —this bound improves the implicit bound of Jamison [9] which is given in terms of the achromatic number: ψ(Gn) ≥ α(Gn) ≥ q +1. We also calculate, precisely, the pseudoachromatic number ...
متن کاملThe Pseudoachromatic Number of a Graph
The pseudoachromatic number of a graph G is the maximum size of a vertex partition of G (where the sets of the partition may or may not be independent) such that, between any two distinct parts, there is at least one edge of G. This parameter is determined for graphs such as cycles, paths, wheels, certain complete multipartite graphs, and for other classes of graphs. Some open problems are raised.
متن کاملAchromatic number versus pseudoachromatic number: a counterexample to a conjecture of Hedetniemi
The pseudoachromatic number of a graph is the largest number of colours in a (not necessarily proper) vertex colouring of the graph such that every pair of distinct colours appears on the endpoints of some edge. The achromatic number is largest number of colours which can be used if the colouring must also be proper. Hedetniemi 7] conjectured that these two parameters are equal for all trees. W...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2017
ISSN: 0166-218X
DOI: 10.1016/j.dam.2017.03.019