Iskanje po katalogu digitalne knjižnice

Iskalni niz:	išči po
	išči po
	išči po
	išči po
Vrsta gradiva:	* po starem in bolonjskem študiju
Jezik:
Išči po:
Opcije:	Prikaži samo zadetke s celotnim besedilom
	Ponastavi

1 - 2 / 2

A new framework to approach Vizing's conjecture
Boštjan Brešar, Bert L. Hartnell, Michael A. Henning, Kirsti Kuenzel, Douglas F. Rall, 2021, izvirni znanstveni članek

Opis: We introduce a new setting for dealing with the problem of the domination number of the Cartesian product of graphs related to Vizing's conjecture. The new framework unifies two different approaches to the conjecture. The most common approach restricts one of the factors of the product to some class of graphs and proves the inequality of the conjecture then holds when the other factor is any graph. The other approach utilizes the so-called Clark-Suen partition for proving a weaker inequality that holds for all pairs of graphs. We demonstrate the strength of our framework by improving the bound of Clark and Suen as follows: ɣ(X◻Y) ≥ max{1/2ɣ(X) ɣt(Y), 1/2ɣt(X) ɣ(Y)}, where ɣ stands for the domination number, ɣt is the total domination number, and X◻Y is the Cartesian product of graphs X and Y.
Ključne besede: Cartesian product, total domination, Vizing's conjecture, Clark and Suen bound
Objavljeno v DKUM: 09.08.2024; Ogledov: 86; Prenosov: 8
Celotno besedilo (179,75 KB)
Gradivo ima več datotek! Več...

Orientable domination in product-like graphs
Sarah Anderson, Boštjan Brešar, Sandi Klavžar, Kirsti Kuenzel, Douglas F. Rall, 2023, izvirni znanstveni članek

Opis: The orientable domination number, ▫${\rm DOM}(G)$▫, of a graph ▫$G$▫ is the largest domination number over all orientations of ▫$G$▫. In this paper, ▫${\rm DOM}$▫ is studied on different product graphs and related graph operations. The orientable domination number of arbitrary corona products is determined, while sharp lower and upper bounds are proved for Cartesian and lexicographic products. A result of Chartrand et al. from 1996 is extended by establishing the values of ▫${\rm DOM}(K_{n_1,n_2,n_3})$▫ for arbitrary positive integers ▫$n_1,n_2$▫ and ▫$n_3$▫. While considering the orientable domination number of lexicographic product graphs, we answer in the negative a question concerning domination and packing numbers in acyclic digraphs posed in [Domination in digraphs and their direct and Cartesian products, J. Graph Theory 99 (2022) 359-377].
Ključne besede: digraph, domination, orientable domination number, packing, graph product, corona graph
Objavljeno v DKUM: 09.08.2023; Ogledov: 446; Prenosov: 39
Celotno besedilo (419,38 KB)
Gradivo ima več datotek! Več...

Iskanje izvedeno v 0.06 sek.

Na vrh