A hamiltonian square-path (-cycle) is one obtained from a hamiltonian path (cycle) by joining every pair of vertices of distance two in the path (cycle). Let G be a graph on n vertices with minimum degree $(G). Posa and Seymour conjectured that if $(G) 2 3 n, then G contains a hamiltonian square-cy
Hamiltonian orthogeodesic alternating paths
β Scribed by Di Giacomo, Emilio; Grilli, Luca; Krug, Marcus; Liotta, Giuseppe; Rutter, Ignaz
- Book ID
- 119292779
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 597 KB
- Volume
- 16
- Category
- Article
- ISSN
- 1570-8667
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## Let G be a 2-connected graph with n vertices such that d(u)+d(u)+d(w)-IN(u)nN(u)nN(w)I an+ 1 holds for any triple of independent vertices u, v and w. Then for any distinct vertices u and u such that {u, 0) is not a cut vertex set of G, there is a hamiltonian path between u and o. In particular,
## Abstract The Hamiltonian path graph __H(G)__ of a graph __G__ is that graph having the same vertex set as __G__ and in which two vertices __u__ and __v__ are adjacent if and only if __G__ contains a Hamiltonian __uβv__ path. A characterization of Hamiltonian graphs isomorphic to their Hamiltonia