Encoding the vertices of a graph with binary edge labels

Zsolt Tuza
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Zsolt Tuza: Hungarian Academy of Sciences, Computer and Automation Institute

A chapter in Sequences, 1990, pp 287-299 from Springer

Abstract: Abstract Let G = (V, E) be an undirected graph with vertex set V and edge set E, and suppose that G does not contain isolated vertices and isolated edges. An assignment f : E → {0, 1} m is called a code of length m if the Boolean sum (or, alternatively, the mod 2 sum) $$ f(\upsilon ): = \sum\limits_{e \in E,\upsilon \in e} {f(e)} $$ is distinct for every vertex υ ∈ V. We prove that every graph has a code of length O(log|V|).

Keywords: Span Tree; Minimum Degree; Edge Label; Span Subgraph; Vertex Label (search for similar items in EconPapers)
Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-3352-7_23

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DOI: 10.1007/978-1-4612-3352-7_23

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