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Upward-closed hereditary families in the dominance order [PDF]

open access: yesDiscrete Mathematics & Theoretical Computer Science, 2022
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 ...
Michael D. Barrus, Jean A. Guillaume
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Conflict-Free Vertex Connection Number At Most 3 and Size of Graphs

open access: yesDiscussiones Mathematicae Graph Theory, 2021
A path in a vertex-coloured graph is called conflict-free if there is a colour used on exactly one of its vertices. A vertex-coloured graph is said to be conflict-free vertex-connected if any two distinct vertices of the graph are connected by a conflict-
Doan Trung Duy, Schiermeyer Ingo
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Spectra of Orders for k-Regular Graphs of Girth g

open access: yesDiscussiones Mathematicae Graph Theory, 2021
A (k, g)-graph is a k-regular graph of girth g. Given k ≥ 2 and g ≥ 3, infinitely many (k, g)-graphs of infinitely many orders are known to exist. Our goal, for given k and g, is the classification of all orders n for which a (k, g)-graph of order n ...
Jajcay Robert, Raiman Tom
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An extremal problem on potentially K_p,1,1-graphic sequences [PDF]

open access: yesDiscrete Mathematics & Theoretical Computer Science, 2005
A sequence S is potentially K_p,1,1 graphical if it has a realization containing a K_p,1,1 as a subgraph, where K_p,1,1 is a complete 3-partite graph with partition sizes p,1,1.
Chunhui Lai
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