Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Hartnell Bert L."'
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 41, Iss 3, Pp 749-762 (2021)
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 restr
Externí odkaz:
https://doaj.org/article/d39ef649a90b4e12858219b3cbc08358
Autor:
Hartnell, Bert L., Rall, Douglas F.
A set $P$ of vertices in a graph $G$ is an open packing if no two distinct vertices in $P$ have a common neighbor. Among all maximal open packings in $G$, the smallest cardinality is denoted $\rho^{\rm o}_L(G)$ and the largest cardinality is $\rho^{\
Externí odkaz:
http://arxiv.org/abs/2006.01616
Publikováno v:
In Discrete Applied Mathematics 15 November 2022 321:261-271
In 1970, Plummer defined a well-covered graph to be a graph $G$ in which all maximal independent sets are in fact maximum. Later Hartnell and Rall showed that if the Cartesian product $G \Box H$ is well-covered, then at least one of $G$ or $H$ is wel
Externí odkaz:
http://arxiv.org/abs/1703.08716
Publikováno v:
In Discrete Applied Mathematics 15 September 2020 283:655-688
Autor:
Hartnell, Bert L., Rall, Douglas F.
A graph is well-covered if every maximal independent set has the same cardinality, namely the vertex independence number. We answer a question of Topp and Volkmann and prove that if the Cartesian product of two graphs is well-covered, then at least o
Externí odkaz:
http://arxiv.org/abs/1204.6681
Autor:
Hartnell, Bert L., Rall, Douglas F.
For a given positive integer t we consider graphs having maximal independent sets of precisely t distinct cardinalities and restrict our attention to those that have no vertices of degree one. In the situation when t is four or larger and the length
Externí odkaz:
http://arxiv.org/abs/1110.4310
Publikováno v:
In Discrete Applied Mathematics 19 June 2017 224:91-105
Publikováno v:
In Discrete Applied Mathematics 31 December 2016 215:71-94
Autor:
Hartnell, Bert L.1 bert.hartnell@smu.ca, Rall, Douglas F.2 doug.rall@furman.edu, Wash, Kirsti3 kwashmath@gmail.com
Publikováno v:
Graphs & Combinatorics. Nov2018, Vol. 34 Issue 6, p1259-1268. 10p.