Home About Upload Latest Additions Statistics Contact
UT Proceedings
UT Student Theses
Dutch Academic Output Dutch Dissertations EU Publications (OpenAIRE)
Printversion
Advanced search

Stars and bunches in planar graphs. Part II: General planar graphs and colourings

Share/Save/Bookmark

Borodin, O.V. and Broersma, H.J. and Glebov, A. and Heuvel van den, J. (2002) Stars and bunches in planar graphs. Part II: General planar graphs and colourings. [Report]

[img]
Preview
PDF
639Kb
Abstract:Given a plane graph, a $k$-star at $u$ is a set of $k$ vertices with a common neighbour $u$; and a bunch is a maximal collection of paths of length at most two in the graph, such that all paths have the same end vertices and the edges of the paths form consecutive edges (\,in the natural order in the plane graph\,) around the two end vertices. We first prove a theorem on the structure of plane graphs in terms of stars and bunches. The result states that a plane graph contains a $(d-1)$-star centred at a vertex of degree $d\leq5$ and the sum of the degrees of the vertices in the star is bounded, or there exists a large bunch.
Item Type:Report
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:
Link to this item:http://purl.utwente.nl/publications/65820
Export this item as:BibTeX
EndNote
HTML Citation
Reference Manager

 

Repository Staff Only: item control page

Metis ID: 208267