- 期刊
NOTES ON SUFFICIENT CONDITIONS FOR A GRAPH TO BE HAMILTONIAN
並列摘要
The first part of this paper deals with an extension of Dirac's Theorem to directed graphs. It is related to a result often referred to as the Ghouila-Houri Theorem. Here we show that the requirement of being strongly connected in the hypothesis of the Ghouila-Houri Theorem is redundant. The Second part of the paper shows that a condition on the number of edges for a graph to be hamiltonian implies Ore's condition on the degrees of the vertices.
延伸閱讀
- Liao, C. S. (2009). Graph-Theoretic Domination and Related Problems with Applications [doctoral dissertation, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2009.10168
- Kohjerdi, F. K., & Bagheri, A. (2012). Hamiltonian Paths in Some Classes of Grid Graphs. Journal of Applied Mathematics, 2012(), 679-695-348. https://doi.org/10.1155/2012/475087
- GIRSE, R. O., & GILLMAN, R. A. (1988). HOMOMORPHISMS AND RELATED CONTRACTIONS OF GRAPHS. International Journal of Mathematics and Mathematical Sciences, 1988(), 95-100. https://doi.org/10.1155/S0161171288000146
- HOPKINS, B. (2004). HAMILTONIAN PATHS ON PLATONIC GRAPHS. International Journal of Mathematics and Mathematical Sciences, 2004(), 1613-1616-119. https://doi.org/10.1155/S0161171204307118
- Lien, H. L. (2010). Two construction schemes for 4-regular 2-fault tolerant hamiltonian graphs [master's thesis, Chung Yuan Christian University]. Airiti Library. https://doi.org/10.6840/cycu201000458