منابع مشابه
Polychromatic Colorings on the Hypercube
Given a subgraph G of the hypercube Qn, a coloring of the edges of Qn such that every embedding of G contains an edge of every color is called a G-polychromatic coloring. The maximum number of colors with which it is possible to G-polychromatically color the edges of any hypercube is called the polychromatic number of G. To determine polychromatic numbers, it is only necessary to consider a str...
متن کاملPolychromatic Colorings of Subcubes of the Hypercube
Alon, Krech, and Szabó [SIAM J. Discrete Math., 21 (2007), pp. 66–72] called an edge-coloring of a hypercube with p colors such that every subcube of dimension d contains every color a d-polychromatic p-coloring. Denote by pd the maximum number of colors with which it is possible to d-polychromatically color any hypercube. We find the exact value of pd for all values of d.
متن کاملLinear Polychromatic Colorings of Hypercube Faces
A coloring of the `-dimensional faces of Qn is called d-polychromatic if every embedded Qd has every color on at least one face. Denote by p `(d) the maximum number of colors such that any Qn can be colored in this way. We provide a new lower bound on p`(d) for ` > 1.
متن کاملEdge-Colorings with No Large Polychromatic Stars
Given a graph G and a positive integer r, let f r (G) denote the largest number of colors that can be used in a coloring of E(G) such that each vertex is incident to at most r colors. For all positive integers n and r, we determine f r (K n;n) exactly and f r (K n) within 1. In doing so, we disprove a conjecture by Manoussakis, Spyratos, Tuza and Voigt in 4].
متن کاملPolychromatic colorings of bounded degree plane graphs
A polychromatic k-coloring of a plane graph G is an assignment of k colors to the vertices of G such that every face of G has all k colors on its boundary. For a given plane graph G, we seek the maximum number k such that G admits a polychromatic k-coloring. We call a k-coloring in the classical sense (i.e., no monochromatic edges) that is also a polychromatic k-coloring a strong polychromatic ...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2018
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2018.v9.n4.a4