Document
type: Class

On the additivity of crossing numbers of graphs
estado: published
has publication venue: Journal of Knot Theory and its Ramifications
type: Continuant
doi: 10.1142/S0218216508006531
related by: authorship_12228
most specific type: Document
type: Entity
type: Document
type: Information Content Entity
most specific type: Article
crisid: 2055
type: Generically Dependent Continuant
type: Thing
date time value: article date 2055
related by: authorship_12229
freetext keyword: Additivity; Crossing numbers; Crossing-critical; Zip product
issue: 9
origen: scopus
e iscopus: 2-s2.0-58149507847
type: Article
abstract: We describe a relationship between the crossing number of a graph G with a 2-edge-cut C and the crossing numbers of the components of G-C. Let G be a connected graph with a 2-edge-cut C := [V1,V2]. Let u 1u2, v1v2 be the edges of C, so that ui,vi ∈ Vi for i = 1,2, and let G i := G[Vi] and G%27i := Gi u ivi. We show that if either G1 or G2 is not connected, then cr(G) = cr(G1) cr(G2), and that if they are both connected then cr(G) = cr(G%271) cr(G%272). We use this to show how to decompose crossing-critical graphs with 2-edge-cuts into smaller, 3-edge-connected crossing-critical graphs. We also observe that this settles a question arising from knot theory, raised by Sawollek, by describing exactly under which conditions the crossing number of the connected sum of two graphs equals the sum of the crossing numbers of the individual graphs. © 2008 World Scientific Publishing Company.
page end: 1050
has funding vehicle: Consejo Nacional de Ciencia y Tecnología, CONACYT: 45903
abstract: We describe a relationship between the crossing number of a graph G with a 2-edge-cut C and the crossing numbers of the components of G-C. Let G be a connected graph with a 2-edge-cut C := [V1,V2]. Let u 1u2, v1v2 be the edges of C, so that ui,vi ∈ Vi for i = 1,2, and let G i := G[Vi] and G%27i := Gi %2b u ivi. We show that if either G1 or G2 is not connected, then cr(G) = cr(G1) %2b cr(G2), and that if they are both connected then cr(G) = cr(G%271) %2b cr(G%272). We use this to show how to decompose crossing-critical graphs with 2-edge-cuts into smaller, 3-edge-connected crossing-critical graphs. We also observe that this settles a question arising from knot theory, raised by Sawollek, by describing exactly under which conditions the crossing number of the connected sum of two graphs equals the sum of the crossing numbers of the individual graphs. © 2008 World Scientific Publishing Company.
abstract: We describe a relationship between the crossing number of a graph G with a 2-edge-cut C and the crossing numbers of the components of G-C. Let G be a connected graph with a 2-edge-cut C := [V1,V2]. Let u 1u2, v1v2 be the edges of C, so that ui,vi ∈ Vi for i = 1,2, and let G i := G[Vi] and G'i := Gi %2b u ivi. We show that if either G1 or G2 is not connected, then cr(G) = cr(G1) %2b cr(G2), and that if they are both connected then cr(G) = cr(G'1) %2b cr(G'2). We use this to show how to decompose crossing-critical graphs with 2-edge-cuts into smaller, 3-edge-connected crossing-critical graphs. We also observe that this settles a question arising from knot theory, raised by Sawollek, by describing exactly under which conditions the crossing number of the connected sum of two graphs equals the sum of the crossing numbers of the individual graphs. © 2008 World Scientific Publishing Company.
accesstype: All Open Access, Green
page start: 1043
volume: 17

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Consejo Nacional de Ciencia y Tecnología, CONACYT: 45903
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type: BFO_0000020
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funding vehicle for: On the additivity of crossing numbers of graphs

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RDF description of On the additivity of crossing numbers of graphs - http://orbis.uaslp.mx/vivo/individual/scopus2054
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date: 2026-08-27T08:17:21
publisher: vivo
type: Document

Article
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Information Content Entity
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Journal of Knot Theory and its Ramifications
publication venue for: On the additivity of crossing numbers of graphs
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type: Continuant
type: Document
type: Information Content Entity
type: Generically Dependent Continuant
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