On induced-universal graphs for the class of bounded-degree graphs

Authors:
Louis Esperet;Arnaud Labourel;Pascal Ochem
Affiliations:
LaBRI, Université de Bordeaux I, 351 Cours de la Liberation, Talence Cedex, France;LaBRI, Université de Bordeaux I, 351 Cours de la Liberation, Talence Cedex, France;LaBRI, Université de Bordeaux I, 351 Cours de la Liberation, Talence Cedex, France
Venue:
Information Processing Letters
Year:
2008

Citing 8
Cited 0

Universal graphs for bounded-degree trees and planar graphs

SIAM Journal on Discrete Mathematics
Universal graphs and induced-universal graphs

Journal of Graph Theory
Implicit representation of graphs

SIAM Journal on Discrete Mathematics
The chromatic number of oriented graphs

Journal of Graph Theory
On universal graphs for planar oriented graphs of a given girth

Discrete Mathematics
Sparse universal graphs for bounded-degree graphs

Random Structures & Algorithms
Optimal simulations of tree machines

SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Coding the vertexes of a graph

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.89

Visualization

Abstract

For a family F of graphs, a graph U is said to be F-induced-universal if every graph of F is an induced subgraph of U. We give a construction for an induced-universal graph for the family of graphs on n vertices with degree at most k. For k even, our induced-universal graph has O(n^k^/^2) vertices and for k odd it has O(n^@?^k^/^2^@?^-^1^/^klog^2^+^2^/^kn) vertices. This construction improves a result of Butler by a multiplicative constant factor for the even case and by almost a multiplicative n^1^/^k factor for the odd case. We also construct induced-universal graphs for the class of oriented graphs with bounded incoming and outgoing degree, slightly improving another result of Butler.