Previous |  Up |  Next

Article

Title: The converse of Kelly’s lemma and control-classes in graph reconstruction (English)
Author: Dulio, Paolo
Author: Pannone, Virgilio
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 44
Issue: 1
Year: 2005
Pages: 25-38
Summary lang: English
.
Category: math
.
Summary: We prove a converse of the well-known Kelly’s Lemma. This motivates the introduction of the general notions of $\mathcal{K}$-table, $\mathcal{K}$-congruence and control-class. (English)
Keyword: Graph
Keyword: Kelly’s Lemma
Keyword: Reconstruction
MSC: 05C05
MSC: 05C60
idZBL: Zbl 1086.05051
idMR: MR2218565
.
Date available: 2009-08-21T06:49:05Z
Last updated: 2012-05-04
Stable URL: http://hdl.handle.net/10338.dmlcz/133380
.
Reference: [1] Bollobás B.: Almost every graph has reconstruction number three.J. Graph Theory 14 (1990), 1–4 Zbl 0702.05061, MR 1037416
Reference: [2] Bondy J. A.: A Graph Reconstructor’s Manual. : Lecture Notes LMS, vol. 166, Cambridge Univ. Press., 1991. MR 1161466
Reference: [3] Dulio P., Pannone V.: Trees with the same path-table.submitted. Zbl 1118.05014
Reference: [4] Geller D., Manvel B.: Reconstruction of cacti.Canad. J. Math. 21 (1969), 1354–1360. Zbl 0187.21401, MR 0252255
Reference: [5] Greenwell D. L., Hemminger R. L.: Reconstructing the $n$-connected components of a graph.Aequationes Math. 9 (1973), 19–22. Zbl 0255.05125, MR 0384614
Reference: [6] Harary F., Plantholt M.: The Graph Reconstruction Number.J. Graph Theory 9 (1985), 451–454. Zbl 0664.05043, MR 0890233
Reference: [7] Kelly P. J.: A congruence Theorem for Trees.Pacific J. Math. 7 (1957), 961–968. Zbl 0078.37103, MR 0087949
Reference: [8] Lauri J.: The reconstruction of maximal planar graphs. II. Reconstruction.J. Combin. Theory, Ser. B 30, 2 (1981), 196–214. Zbl 0413.05036, MR 0615314
Reference: [9] Lauri J.: Graph reconstruction-some techniques and new problems.Ars Combinatoria, ser. B 24 (1987), 35–61. Zbl 0659.05068, MR 0941788
Reference: [10] Monson S. D.: The reconstruction of cacti revisited.Congr. Numer. 69 (1989), 157–166. Zbl 0678.05040, MR 0995883
Reference: [11] Nýdl V.: Finite undirected graphs which are not reconstructible from their large cardinality subgraphs.Discrete Math. 108 (1992), 373–377. Zbl 0759.05067, MR 1189858
Reference: [12] Tutte W. T.: All the king’s horses. A guide to reconstruction.In: Graph Theory and Related Topics, Acad. Press, New York, 1979 (pp. 15–33). Zbl 0472.05046, MR 0538033
.

Files

Files Size Format View
ActaOlom_44-2005-1_4.pdf 408.7Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo