The k-dimensional cube is k-representable

Bas Broere, Hans Zantema

Uittreksel

A graph is called k-representable if there exists a word w over the nodes of the graph, each node occurring exactly k times, such that there is an edge between two nodes x, y if and only after removing all letters distinct from x, y, from w, a word remains in which x, y alternate. We prove that if G is k-representable for k > 1, then the Cartesian product of G and the complete graph on n nodes is (k + n − 1)-representable. As a direct consequence, the k-dimensional cube is k-representable for every k ≥ 1. Our main technique consists of exploring occurrence-based functions that replace every ith occurrence of a symbol x in a word w by a string h(x, i). The representing word we construct to achieve our main theorem is purely composed from concatenation and occurrence-based functions
Taal Engels 3-12 10 Journal of Automata, Languages and Combinatorics 24 1 10.25596/jalc-2019-003 Gepubliceerd - 2019

Vingerafdruk

Regular hexahedron
Cartesian product
Vertex of a graph
Product Graph
Concatenation
Graph in graph theory
Complete Graph
Alternate
Strings
Distinct
Theorem

Citeer dit

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In: Journal of Automata, Languages and Combinatorics, Vol. 24, Nr. 1, 2019, blz. 3-12.

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