Zobrazeno 1 - 10
of 85
pro vyhledávání: '"Trenk, Ann N."'
A graph with degree sequence $\pi$ is a \emph{unigraph} if it is isomorphic to every graph that has degree sequence $\pi$. The class of unigraphs is not hereditary and in this paper we study the related hereditary class HCU, the hereditary closure of
Externí odkaz:
http://arxiv.org/abs/2308.12190
In this paper, we study split graphs and related classes of graphs from the perspective of their sequence of vertex degrees and an associated lattice under majorization. Following the work of Merris in 2003, we define blocks $[\alpha(\pi)|\beta(\pi)]
Externí odkaz:
http://arxiv.org/abs/2211.02170
Publikováno v:
In Discrete Mathematics April 2024 347(4)
Autor:
Anderson, Sarah E., Collins, Karen L., Ferrero, Daniela, Hogben, Leslie, Mayer, Carolyn, Trenk, Ann N., Walker, Shanise
Throttling addresses the question of minimizing the sum or the product of the resources used to accomplish a task and the time needed to complete that task for various graph searching processes. Graph parameters of interest include various types of z
Externí odkaz:
http://arxiv.org/abs/2012.12807
Autor:
Anderson, Sarah E., Collins, Karen L., Ferrero, Daniela, Hogben, Leslie, Mayer, Carolyn, Trenk, Ann N., Walker, Shanise
The product power throttling number of a graph is defined to study product throttling for power domination. The domination number of a graph is an upper bound for its product power throttling number. It is established that the two parameters are equa
Externí odkaz:
http://arxiv.org/abs/2010.16315
Rabinovitch showed in 1978 that the interval orders having a representation consisting of only closed unit intervals have order dimension at most 3. This article shows that the same dimension bound applies to two other classes of posets: those having
Externí odkaz:
http://arxiv.org/abs/2004.08294
Autor:
Collins, Karen L., Trenk, Ann N.
In this paper we introduce the concepts of the distinguishing number and the distinguishing chromatic number of a poset. For a distributive lattice $L$ and its set $Q_L$ of join-irreducibles, we use classic lattice theory to show that any linear exte
Externí odkaz:
http://arxiv.org/abs/1905.09858
In this paper we combine ideas from tolerance orders with recent work on OC interval orders. We consider representations of posets by unit intervals $I_v$ in which the interval endpoints ($L(v)$ and $R(v)$) may be open or closed as well as the center
Externí odkaz:
http://arxiv.org/abs/1707.08099
A poset $P = (X,\prec)$ has an interval representation if each $x \in X$ can be assigned a real interval $I_x$ so that $x \prec y$ in $P$ if and only if $I_x$ lies completely to the left of $I_y$. Such orders are called \emph{interval orders}. In thi
Externí odkaz:
http://arxiv.org/abs/1707.08093
Autor:
Collins, Karen L., Trenk, Ann N.
A graph is a split graph if its vertex set can be partitioned into a clique and a stable set. A split graph is unbalanced if there exist two such partitions that are distinct. Cheng, Collins and Trenk (2016), discovered the following interesting coun
Externí odkaz:
http://arxiv.org/abs/1706.03092