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pro vyhledávání: '"Barrus, Michael D."'
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
The distinguishing chromatic number of a graph $G$ is the smallest number of colors needed to properly color the vertices of $G$ so that the trivial automorphism is the only symmetry of $G$ that preserves the coloring. We investigate the distinguishi
Externí odkaz:
http://arxiv.org/abs/2303.13759
Autor:
Barrus, Michael D., Haronian, Nathan
The realization graph $\mathcal{G}(d)$ of a degree sequence $d$ is the graph whose vertices are labeled realizations of $d$, where edges join realizations that differ by swapping a single pair of edges. Barrus [On realization graphs of degree sequenc
Externí odkaz:
http://arxiv.org/abs/2201.04730
Autor:
Barrus, Michael D.
The Erd\H{o}s--Gallai criteria for recognizing degree sequences of simple graphs involve a system of inequalities. Given a fixed degree sequence, we consider the list of differences of the two sides of these inequalities. These differences have appea
Externí odkaz:
http://arxiv.org/abs/2107.07643
We give a characterization of the graphs with at most three trivial characteristic ideals. This implies the complete characterization of the regular graphs whose critical groups have at most three invariant factors equal to 1 and the characterization
Externí odkaz:
http://arxiv.org/abs/2004.00172
Autor:
Barrus, Michael D., Guillaume, Jean A.
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 23, no. 3, Graph Theory (January 20, 2022) dmtcs:5666
The majorization relation orders the degree sequences of simple graphs into posets called dominance orders. As shown by Ruch and Gutman (1979) and Merris (2002), the degree sequences of threshold and split graphs form upward-closed sets within the do
Externí odkaz:
http://arxiv.org/abs/1905.09411
Autor:
Barrus, Michael D., Haronian, Nathan
Publikováno v:
In Discrete Mathematics January 2023 346(1)
Autor:
Barrus, Michael D., Sinkovic, John
Publikováno v:
Discrete Mathematics, vol. 341 (2018), no. 7, pp. 1973-1982
The tree-depth of $G$ is the smallest value of $k$ for which a labeling of the vertices of $G$ with elements from $\{1,\dots,k\}$ exists such that any path joining two vertices with the same label contains a vertex having a higher label. The graph $G
Externí odkaz:
http://arxiv.org/abs/1704.07311
Autor:
Barrus, Michael D.
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol. 20 no. 1, Graph Theory (June 4, 2018) dmtcs:3968
We define a weakly threshold sequence to be a degree sequence $d=(d_1,\dots,d_n)$ of a graph having the property that $\sum_{i \leq k} d_i \geq k(k-1)+\sum_{i > k} \min\{k,d_i\} - 1$ for all positive $k \leq \max\{i:d_i \geq i-1\}$. The weakly thresh
Externí odkaz:
http://arxiv.org/abs/1608.01358