## Abstract Sufficient degree conditions for the existence of properly edgeβcolored cycles and paths in edgeβcolored graphs, multigraphs and random graphs are investigated. In particular, we prove that an edgeβcolored multigraph of order __n__ on at least three colors and with minimum colored degre
The number of Hamiltonian paths and cycles on k-colored graphs
β Scribed by David A Klarner
- Publisher
- Elsevier Science
- Year
- 1969
- Weight
- 239 KB
- Volume
- 72
- Category
- Article
- ISSN
- 1385-7258
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The hamiltonian path graph H(F) of a graph F is that graph having the same vertex set as F and in which two vertices u and u are adjacent if and only if F contains a hamiltonian u -u path. First, in response to a conjecture of Chartrand, Kapoor and Nordhaus, a characterization of nonhamiltonian grap
## Abstract We consider the problem of the minimum number of Hamiltonian cycles that could be present in a Hamiltonian maximal planar graph on __p__ vertices. In particular, we construct a __p__βvertex maximal planar graph containing exactly four Hamiltonian cycles for every __p__ β₯ 12. We also pro
It is shown that, if t is an integer !3 and not equal to 7 or 8, then there is a unique maximal graph having the path P t as a star complement for the eigenvalue Γ2: The maximal graph is the line graph of K m,m if t ΒΌ 2mΓ1, and of K m,m ΓΎ1 if t ΒΌ 2m. This result yields a characterization of L(G ) wh
It is proved that if a planar triangulation different from K3 and K4 contains a Hamiltonian cycle, then it contains at least four of them. Together with the result of Hakimi, Schmeichel, and Thomassen [21, this yields that, for n 2 12, the minimum number of Hamiltonian cycles in a Hamiltonian planar