Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9512201 | Discrete Mathematics | 2005 | 14 Pages |
Abstract
A graph G=(V,E) is called a split graph if there exists a partition V=IâªK such that the subgraphs of G induced by I and K are empty and complete graphs, respectively. In 1980, Burkard and Hammer gave a necessary but not sufficient condition for hamiltonian split graphs with |I|<|K|. In this paper, we show that the Burkard-Hammer condition is also sufficient for the existence of a Hamilton cycle in a split graph G such that 5â |I|<|K| and the minimum degree δ(G)⩾|I|-3. For the case 5=|I|<|K|, all split graphs satisfying the Burkard-Hammer condition but having no Hamilton cycles are also described.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Ngo Dac Tan, Le Xuan Hung,