On vertex-degree restricted subgraphs in polyhedral graphs

Authors:
Igor Fabrici
Affiliations:
Department of Mathematics, Technical University Ilmenau, PF 10 0565, D-98684 Ilmenau, Germany
Venue:
Discrete Mathematics
Year:
2002

Citing 6
Cited 1

Subgraphs with restricted degrees of their vertices in planar graphs

Discrete Mathematics
On light cycles in plane triangulations

Discrete Mathematics
On 3-connected plane graphs without triangular faces

Journal of Combinatorial Theory Series B
On vertex-degree restricted paths in polyhedral graphs

Discrete Mathematics
Connected subgraphs with small degree sums in 3-connected planar graphs

Journal of Graph Theory
Light paths in 4-connected graphs in the plane and other surfaces

Journal of Graph Theory

On light graphs in the family of 4-connected planar graphs

Discrete Mathematics

Quantified Score

Hi-index	0.05

Visualization

Abstract

First a brief survey of known facts is given. Main result of this paper: every polyhedral (i.e. 3-connected planar) graph G with minimum degree at least 4 and order at least k (k ≤ 4) contains a connected subgraph on k vertices having degrees (in G) at most 4k - 1, the bound 4k- 1 being best possible.