TY - GEN

T1 - Adjacency labeling schemes and induced-universal graphs

AU - Alstrup, Stephen

AU - Kaplan, Haim

AU - Thorup, Mikkel

AU - Zwick, Uri

N1 - Publisher Copyright:
© Copyright 2015 ACM.

PY - 2015/6/14

Y1 - 2015/6/14

N2 - We describe a way of assigning labels to the vertices of any undirected graph on up to n vertices, each composed of n/2+ O(1) bits, such that given the labels of two vertices, and no other information regarding the graph, it is possible to decide whether or not the vertices are adjacent in the graph. This is optimal, up to an additive constant, and constitutes the first improvement in almost 50 years of an n/2+O(log n) bound of Moon. As a consequence, we obtain an induced-universal graph for n-vertex graphs containing only O(2n/2) vertices, which is optimal up to a multiplicative constant, solving an open problem of Vizing from 1968. We obtain similar tight results for directed graphs, tournaments and bipartite graphs.

AB - We describe a way of assigning labels to the vertices of any undirected graph on up to n vertices, each composed of n/2+ O(1) bits, such that given the labels of two vertices, and no other information regarding the graph, it is possible to decide whether or not the vertices are adjacent in the graph. This is optimal, up to an additive constant, and constitutes the first improvement in almost 50 years of an n/2+O(log n) bound of Moon. As a consequence, we obtain an induced-universal graph for n-vertex graphs containing only O(2n/2) vertices, which is optimal up to a multiplicative constant, solving an open problem of Vizing from 1968. We obtain similar tight results for directed graphs, tournaments and bipartite graphs.

KW - Adjacency labeling schemes

KW - Induced-universal graphs

UR - http://www.scopus.com/inward/record.url?scp=84958751997&partnerID=8YFLogxK

U2 - 10.1145/2746539.2746545

DO - 10.1145/2746539.2746545

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AN - SCOPUS:84958751997

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 625

EP - 634

BT - STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing

PB - Association for Computing Machinery

T2 - 47th Annual ACM Symposium on Theory of Computing, STOC 2015

Y2 - 14 June 2015 through 17 June 2015

ER -