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On the time required to recognize properties of graphs: a problem

On the time required to recognize properties of graphs: a problem SIGACT News October ON THE TIME REQUIRED TO RECOGNIZE PROPERTIES OF GRAPHS: A Problem Arnold L. Rosenberg Mathematical Sciences Department IBM Watson Research Center Yorktown Heights, New York In a recent paper H-R Theorems. which, [i], Holt and Reingold have proved the following results. Let graphs be presented via their incidence matrices. Any algorithm given an n-node graph, (resp., contains detects whether or not the graph is strongly case probe 0(n 2) entries connected a cycle) must in the worst of the incidence matrix. Here, a "probe" is used to detect the presence or absence of edge attractive . A glance at a proof of these results conjecture. Definition. (a) A property For each P renders the following of graphs is natural if is true of some n-node graph and false of naN, P some n-node graph. (b) P is invariant under graph-isomorphism (= renaming of nodes). Let False Conjecture. P Let graphs be presented via their incidence matrices. of graphs. Any algorithm which, property P be any natural property given an n-node must in the worst graph, detects whether or not the graph enjoys 0(n 2) entries case probe of the incidence matrix. Our lack Ray Strong http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGACT News Association for Computing Machinery

On the time required to recognize properties of graphs: a problem

ACM SIGACT News , Volume 5 (4) – Oct 1, 1973

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Publisher
Association for Computing Machinery
Copyright
Copyright © 1973 by ACM Inc.
ISSN
0163-5700
DOI
10.1145/1008299.1008302
Publisher site
See Article on Publisher Site

Abstract

SIGACT News October ON THE TIME REQUIRED TO RECOGNIZE PROPERTIES OF GRAPHS: A Problem Arnold L. Rosenberg Mathematical Sciences Department IBM Watson Research Center Yorktown Heights, New York In a recent paper H-R Theorems. which, [i], Holt and Reingold have proved the following results. Let graphs be presented via their incidence matrices. Any algorithm given an n-node graph, (resp., contains detects whether or not the graph is strongly case probe 0(n 2) entries connected a cycle) must in the worst of the incidence matrix. Here, a "probe" is used to detect the presence or absence of edge attractive . A glance at a proof of these results conjecture. Definition. (a) A property For each P renders the following of graphs is natural if is true of some n-node graph and false of naN, P some n-node graph. (b) P is invariant under graph-isomorphism (= renaming of nodes). Let False Conjecture. P Let graphs be presented via their incidence matrices. of graphs. Any algorithm which, property P be any natural property given an n-node must in the worst graph, detects whether or not the graph enjoys 0(n 2) entries case probe of the incidence matrix. Our lack Ray Strong

Journal

ACM SIGACT NewsAssociation for Computing Machinery

Published: Oct 1, 1973

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