Displaying similar documents to “More forbidden minors for wye-delta-wye reducibility.”

A characterization of diameter-2-critical graphs with no antihole of length four

Teresa Haynes, Michael Henning (2012)

Open Mathematics

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A graph G is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. In this paper we characterize the diameter-2-critical graphs with no antihole of length four, that is, the diameter-2-critical graphs whose complements have no induced 4-cycle. Murty and Simon conjectured that the number of edges in a diameter-2-critical graph of order n is at most n 2/4 and that the extremal graphs are complete bipartite graphs with equal size partite sets. As...

A maximum degree theorem for diameter-2-critical graphs

Teresa Haynes, Michael Henning, Lucas Merwe, Anders Yeo (2014)

Open Mathematics

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A graph is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. Let G be a diameter-2-critical graph of order n. Murty and Simon conjectured that the number of edges in G is at most ⌊n 2/4⌋ and that the extremal graphs are the complete bipartite graphs K ⌊n/2⌋,⌊n/2⌉. Fan [Discrete Math. 67 (1987), 235–240] proved the conjecture for n ≤ 24 and for n = 26, while Füredi [J. Graph Theory 16 (1992), 81–98] proved the conjecture for n > n 0 where...

Eternal Domination: Criticality and Reachability

William F. Klostermeyer, Gary MacGillivray (2017)

Discussiones Mathematicae Graph Theory

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We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached. The study of the stronger assertion that such a set can be reached after a single attack is defended leads to the study of graphs which are critical in the sense that deleting any vertex reduces the eternal domination number. Examples of these graphs...

Ramseyan properties of graphs.

DeLaVina, Ermelinda, Fajtlowicz, Siemion (1996)

The Electronic Journal of Combinatorics [electronic only]

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