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Results tagged with hamiltonian-graphs
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user 29783
A Hamiltonian graph (directed or undirected) is a graph that contains a Hamiltonian cycle, that is, a cycle that visits every vertex exactly once.
10
votes
2
answers
771
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Graphs with many edges avoided by Hamiltonian cycles
Let $G$ be a $3$-connected Hamiltonian graph with at least one edge that belongs to each H-cycle of $G$. Some authors (e.g. in the link given here) call such an edge an a-edge and an edge that belongs …
- 13.4k
11
votes
1
answer
326
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How many edges can be added to two circles before the graph becomes Hamiltonian?
Start with two $n$-circles $(v_1\cdots v_n)$ and $(w_1\cdots w_n)$ of vertice sets $V$ and $W$, where $n\ge 5$. Add a number of vertex-disjoint edges between $V$ and $W$ (thus no chords) in a way tha …
- 13.4k
6
votes
0
answers
73
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Cage graphs and even cycles
Let $G$ be a $(\nu,g)$-cage graph of degree $\nu$ with girth $g$ and $n=n(\nu,g)$ vertices.
Based on the known examples, I am wondering if the following can be proved/disproved:
Is it true that …
- 13.4k