The Edit Distance Function and Symmetrization

Martin, Ryan

doi:10.37236/2262

Cited by 9 publications

(29 citation statements)

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“…Proposition 6 ( [13]). Let p ∈ (0, 1/2) and K be a p-core CRG with black vertices and white or gray edges.…”

Section: Definitions and Toolsmentioning

confidence: 99%

The edit distance function of some graphs

Hu¹,

Shi²,

Wei³

2020

Discuss. Math. Graph Theory

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The edit distance function of a hereditary property H is the asymptotically largest edit distance between a graph of density p ∈ [0, 1] and H . Denote by P n and C n the path graph of order n and the cycle graph of order n, respectively. Let C * 2n be the cycle graph C 2n with a diagonal, and C n be the graph with vertex set {v 0 , v 1 , . . . , v n−1 } andMarchant and Thomason determined the edit distance function of C * 6 . Peck studied the edit distance function of C n , while Berikkyzy et al. studied the edit distance of powers of cycles. In this paper, by using the methods of Peck and Martin, we determine the edit distance function of C * 8 , C n and P n , respectively.

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“…Proposition 6 ( [13]). Let p ∈ (0, 1/2) and K be a p-core CRG with black vertices and white or gray edges.…”

Section: Definitions and Toolsmentioning

confidence: 99%

The edit distance function of some graphs

Hu¹,

Shi²,

Wei³

2020

Discuss. Math. Graph Theory

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“…The symmetrization method obtains lower bounds for ed H (p). The main tools are Lemmas 6 and 7, found in [12]. We have already seen much of the theoretical underpinnings.…”

Section: The P-coresmentioning

confidence: 99%

“…Let b be the black vertex and K = K − {b} and k = |V (K )|. Since K is a clique with all white vertices and all black edges (if any), Proposition 9 from [12] gives that, for p ∈ [1/2, 1), g K (p) = 1 − p + 2p−1 k > 1 − p. By Theorem 11, g K (p) > (1 − p)/2, a contradiction. From now on, we will assume that K has only white vertices and, since it is p-core for p ≥ 1/2, all edges are black or gray.…”

Section: Forb(h 9 )mentioning

confidence: 99%

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On the computation of edit distance functions

Martin

2015

Discrete Mathematics

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The edit distance between two graphs on the same labeled vertex set is the size of the symmetric difference of the edge sets. The edit distance function of the hereditary property, $\mathcal{H}$, is a function of $p\in[0,1]$ and is the limit of the maximum normalized distance between a graph of density $p$ and $\mathcal{H}$. This paper uses the symmetrization method of Sidorenko in order to compute the edit distance function of various hereditary properties. For any graph $H$, ${\rm Forb}(H)$ denotes the property of not having an induced copy of $H$. We compute the edit distance function for ${\rm Forb}(H)$, where $H$ is any split graph, and the graph $H_9$, a graph first used to describe the difficulties in computing the edit distance function.Comment: 25 pages, 2 figure

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“…Two other results that are essential to establishing lower bounds for the edit distance functions of Forb(K 2,t ) appears as lemmas in [33].…”

Section: Select Review Of the Literature And Past Resultsmentioning

confidence: 99%

The edit distance function for graphs: an exploration of the case of forbidden induced K<sub>2,t</sub> and other questions

McKay

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First and foremost, I would like to thank my adviser Ryan Martin for all of his guidance, insight, and encouragement throughout the process of completing this thesis. I would also like to thank all of the members of my POS Committee for their help, support, and valuable advice. In particular, I would like to thank Prof. Hogben for her feedback on the manuscript of this thesis, Prof. Song for important discussions about strongly regular graphs (including directing me to Andries Brouwer's website), and Maria Axenovich for pointing me in the direction of Zolán Füredi's K 2,t-free constructions. Ed Marchant, Andrew Thomason, and Stephen Hartke also contributed helpful conversations and information to my adviser, which he, in turn, passed along to me. In addition, I would like to thank the Mathematics Department at Iowa State for giving me the chance to participate in so many enriching opportunities during my time here, and for both travel support and a semester of research on the Wolfe Research Fellowship.

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The Edit Distance Function and Symmetrization

Cited by 9 publications

References 20 publications

The edit distance function of some graphs

The edit distance function of some graphs

On the computation of edit distance functions

The edit distance function for graphs: an exploration of the case of forbidden induced K<sub>2,t</sub> and other questions

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