We prove that, with some exceptions, every digraph with n 3 9 vertices and at least ( n -1) ( n -2) + 2 arcs contains all orientations of a Hamiltonian cycle.
Cycles of Prescribed Modularity in Planar Digraphs
β Scribed by Anna Galluccio; Martin Loebl
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 252 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0196-6774
No coin nor oath required. For personal study only.
β¦ Synopsis
We present a polynomial-time algorithm to find out whether all directed cycles in a directed planar graph are of length p mod q, with 0 F pq.
π SIMILAR VOLUMES
denote the set of all m Γ n {0, 1}-matrices with row sum vector R and column sum vector S. Suppose A(R, S) ] ". The interchange graph G(R, S) of A(R, S) was defined by Brualdi in 1980. It is the graph with all matrices in A(R, S) as its vertices and two matrices are adjacent provided they differ by
Let D=(V, E) be a digraph with vertex set V of size n and arc set E. For u # V, let d(u) denote the degree of u. A Meyniel set M is a subset of V such that d(u)+d(v) 2n&1 for every pair of nonadjacent vertices u and v belonging to M. In this paper we show that if D is strongly connected, then every
## Abstract Let __G__ be a graph on __p__ vertices with __q__ edges and let __r__β=β__q__βββ__p__β=β1. We show that __G__ has at most ${15\over 16} 2^{r}$ cycles. We also show that if __G__ is planar, then __G__ has at most 2^__r__βββ1^β=β__o__(2^__r__βββ1^) cycles. The planar result is best possib
## 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
We prove that Woodall's and GhouileHouri's conditions on degrees which ensure that a digraph is Hamiltonian, also ensure that it contains the analog of a directed Hamiltonian cycle but with one edge pointing the wrong way; that is, it contains two vertices that are connected in the same direction by