A sequence d = (d1, d2, ..., dn) is graphic if there is a simple graph G with degree sequence d, and such a graph G is called a realization of d. A graphic sequence d is line-hamiltonian if d has a realization G such that L (G) is hamiltonian, and is supereulerian if d has a realization G with a spanning eulerian subgraph. In this paper, it is proved that a nonincreasing graphic sequence d = (d1, d2, ..., dn) has a supereulerian realization if and only if dn ≥ 2 and that d is line-hamiltonian if and only if either d1 = n - 1, or ∑di = 1 di ≤ ∑dj ≥ 2 (dj - 2).
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics