Paths of low weight in planar graphs

• Autorzy: Igor Fabrici , Jochen Harant , Stanislav Jendrol'
• Języki publikacji: EN

Abstrakty

EN

The existence of paths of low degree sum of their vertices in planar graphs is investigated. The main results of the paper are:
1. Every 3-connected simple planar graph G that contains a k-path, a path on k vertices, also contains a k-path P such that for its weight (the sum of degrees of its vertices) in G it holds
$w_G(P): = ∑_{u∈ V(P)} deg_G(u) ≤ (3/2)k² + 𝓞(k)$
2. Every plane triangulation T that contains a k-path also contains a k-path P such that for its weight in T it holds
$w_T(P): = ∑_{u∈ V(P)} deg_T(u) ≤ k² +13 k$
3. Let G be a 3-connected simple planar graph of circumference c(G). If c(G) ≥ σ| V(G)| for some constant σ > 0 then for any k, 1 ≤ k ≤ c(G), G contains a k-path P such that
$w_G(P) = ∑_{u∈ V(P)} deg_G(u) ≤ (3/σ + 3)k$.

Słowa kluczowe

EN

planar graphs; polytopal graphs; paths; weight of an edge; weight of a path

Kategorie tematyczne

• 05C10: Planar graphs; geometric and topological aspects of graph theory
• 05C38: Paths and cycles
• 52B10: Three-dimensional polytopes

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2008
• Tom: 28
• Numer: 1
• Strony: 121-135

Daty

wydano

2008

otrzymano

2006-11-22

poprawiono

2007-05-04

zaakceptowano

2007-05-04

Twórcy

autor

Igor Fabrici

• Institute of Mathematics, P.J. Šafárik University, Jesenná 5, SK-04154 Košice, Slovak Republic

autor

Jochen Harant

• Institute of Mathematics, Ilmenau Technical University, PF 10 05 65, D-98684 Ilmenau, Germany

autor

Stanislav Jendrol'

• Institute of Mathematics, P.J. Šafárik University, Jesenná 5, SK-04154 Košice, Slovak Republic

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1396