Weak k-reconstruction of Cartesian products

Wilfried Imrich (Author), Blaž Zmazek (Author), Janez Žerovnik (Author)

Abstract

Po Ulamovi domnevi je mogoče vsak končen graf ▫$G$▫ rekonstruirati iz množice vseh podgrafov ▫$G$▫ brez ene točke. Znano je, da je mogoče rekonstruirati kartezične produkte. Obravnavan je soroden problem, imenovan šibka rekonstrukcija. Dokazano je, da je mogoče odločiti, ali se da dani graf ▫$H$▫ dobiti iz nekega kartezičnega produkta ▫$g$▫ z odstranitvijo ▫$k$▫ točk, če privzamemo, da ima ▫$G$▫ vsaj ▫$k+1$▫ faktorjev s po ▫$k+1$▫ točkami. V tem rimeru ▫$H$▫ enolično določa ▫$G$▫. Dan je tudi protiprimer za MacAvaneyjevo domnevo.

Keywords

matematika;teorija grafov;kartezični produkt;problem rekonstrukcije;sestavljeni grafi;mathematics;graph theory;reconstruction problem;Cartesian product;composite graphs;

Data

Language:	English
Year of publishing:	2003
Typology:	1.01 - Original Scientific Article
Organization:	UM FS - Faculty of Mechanical Engineering
UDC:	519.17
COBISS:	12632409
ISSN:	1234-3099
Views:	1020
Downloads:	323
Average score:	0 (0 votes)
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Other data

Secondary language:	Slovenian
Secondary title:	Šibka k-rekonstrukcija kartezičnih produktov
Secondary abstract:	By Ulam's conjecture every finite graph ▫$G$▫ can be reconstructed from its deck of vertex deleted subgraphs. The conjecture is still open, but many special cases have been settled. In particular, one can reconstruct Cartesian products. We consider the case of ▫$k$▫-vertex deleted subgraphs of Cartesian products and prove that one can decide whether a graph ▫$H$▫ is a ▫$k$▫-vertex deleted subgraph of a Cartesian product ▫$G$▫ with at least ▫$k+1$▫ prime factors on at least ▫$k+1$▫ vertices each, and that ▫$H$▫ uniquely determines ▫$G$▫. This extends previous works of the authors and Sims. This paper also contains a counterexample to a conjecture of MacAvaney.
Secondary keywords:	matematika;teorija grafov;kartezični produkt;problem rekonstrukcije;sestavljeni grafi;
URN:	URN:SI:UM:
Type (COBISS):	Scientific work
Pages:	str. 273-285
Volume:	ǂVol. ǂ21
Issue:	ǂno. ǂ2
Chronology:	2003
ID:	9595950