Tournaments as strong subcontractions

Jagger, Chris

doi:10.1016/s0012-365x(97)81803-1

Cited by 5 publications

(3 citation statements)

References 9 publications

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“…So, once again, Do F if and only if F can be obtained from D by a sequence of vertex and edge deletions and edge contractions. This definition of contraction for digraphs is very close to that for undirected graphs; other definitions, placing different conditions on the subgraphs D[W u ], are discussed by Jagger [15].…”

Section: Introductionmentioning

confidence: 73%

The Extremal Function for Complete Minors

Thomason

2001

Journal of Combinatorial Theory, Series B

236

224

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Section: Introductionmentioning

confidence: 73%

The Extremal Function for Complete Minors

Thomason

2001

Journal of Combinatorial Theory, Series B

236

224

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“…We note that the operation of taking minors of directed graphs described by [11] corresponds to the weak subcontraction of Jagger [13]. Jagger also defines strong subcontraction as a generalization of undirected graph minors to directed graphs.…”

Section: Vertex Expansion and Graph Minorsmentioning

confidence: 99%

Intrinsically knotted and 4-linked directed graphs

Fleming

Foisy

2018

J. Knot Theory Ramifications

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We consider intrinsic linking and knotting in the context of directed graphs. We construct an example of a directed graph that contains a consistently oriented knotted cycle in every embedding. We also construct examples of intrinsically 3-linked and 4-linked directed graphs. We introduce two operations, consistent edge contraction and H-cyclic subcontraction, as special cases of minors for digraphs, and show that the property of having a linkless embedding is closed under these operations. We analyze the relationship between the number of distinct knots and links in an undirected graph G and its corresponding symmetric digraph DG. Finally, we note that the maximum number of edges for a graph that is not intrinsically linked is O(n) in the undirected case, but O(n 2 ) for directed graphs.

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“…In this paper we shall be looking at corresponding results for containing topological complete digraphs. For results about subcontractions of digraphs, see [7] and [8].…”

Section: Introductionmentioning

confidence: 99%

Extremal Digraph Results for Topological Complete Subgraphs

Jagger

1998

European Journal of Combinatorics

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We determine, to within a constant factor, the maximum size of a digraph that does not contain a topological complete digraph DK p of order p. Let t 1 ( p) be defined for positive p bywhere D denotes a digraph. We show that 1 16 p 2 < t 1 ( p) ≤ 44 p 2 . We also obtain results for containing topological tournaments, and a Turán-type result for containing a topological transitive tournament and a transitive tournament.

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Tournaments as strong subcontractions

Cited by 5 publications

References 9 publications

The Extremal Function for Complete Minors

The Extremal Function for Complete Minors

Intrinsically knotted and 4-linked directed graphs

Extremal Digraph Results for Topological Complete Subgraphs

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