## Abstract We give necessary and sufficient conditions for the existence of an alternating Hamiltonian cycle in a complete bipartite graph whose edge set is colored with two colors.
Hamiltonian cycles in bipartite graphs
β Scribed by Xiaoyun Lu
- Publisher
- Springer-Verlag
- Year
- 1995
- Tongue
- English
- Weight
- 389 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We prove the following theorem. "I'neorem. If G is a balanced bipartite graph with bipartition (A, B), [A I = IBI = n, such that for any x ~ A, y ~ B, d(x) + d(y) >>-n + 2, then for any (nl, n2), ni >I 2, n -----n I + hE, G contains two independent cycles of lengths 2nl and 2n2.
The main result of this paper is the NP-completeness of the HAMILTONIAN CIRCUIT problem for chordal bipartite graphs. This is proved by a sophisticated reduction from SATISFIABILITY. As a corollary, HAMILTONIAN CIRCUIT is NP-complete for strongly chordal split graphs. On both classes the complexity
We prove that if a graph G on n > 32 vertices is hamiltonian and has two nonadjacent vertices u and u with d(u) + d(u) 3 n + z where z = 0 if n is odd and z = 1 if n is even, then G contains all cycles of length m where 3 < m < 1/5(n + 13).
Flandrin et ai. (to appear) define a simple bipartite graph to be biclaw-free if it contains no induced subgraph isomorphic to H, where H could be obtained from two copies of K1.3 by adding an edge joining the two vertices of degree 3. They have shown that if G is a bipartite, balanced, biclaw-free