Outerplanarity of line graphs and iterated line graphs
β Scribed by Huiqiu Lin; Weihua Yang; Hailiang Zhang; Jinlong Shu
- Book ID
- 108052640
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 382 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0893-9659
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## Abstract A graph __G__ is __k__βordered if for every ordered sequence of __k__ vertices, there is a cycle in __G__ that encounters the vertices of the sequence in the given order. We prove that if __G__ is a connected graph distinct from a path, then there is a number __t~G~__ such that for ever
## Dedlcared m my father on his 64th birthday of In this paper, the problem of determining graphs which are switching cqulvaknt to at least their iterated lme graphs is considered, and such connected graphs are characterized.
For a connected graph H of order at least 3, the H-line graph HL(G) of a graph G is defined as that graph whose vertices are the edges of G and where two vertices of HL(G) are adjacent if and only if the corresponding edges of G are adjacent and belong to a common copy of H. For k >~ 2, the kth ite
Given a simple undirected graph G, a spanning subgraph S is a t-spanner of G if every pair of vertices that are adjacent in G are at distance at most I in S. The factor t is called the dilution of the spanner. If S has the smallest possible number of edges among all t-spanners of G, then S is a mini