A homeomorphically irreducible spanning tree or HIST is a spanning tree without vertices of degree 2. A graph not containing a HIST is HIST-free. A graph G is HIST-critical if it is HIST-free and G-v contains a HIST for every vertex v of G.
The graph lists are currently only available in 'graph6' format.
The following lists are available:
All results were obtained with the program HistChecker , see [1] for details.
Vertices | Girth ≥ 3 | Girth ≥ 4 | Girth ≥ 5 | Girth ≥ 6 | Girth ≥ 7 |
---|---|---|---|---|---|
3 | 1 | 0 | 0 | 0 | 0 |
4 | 0 | 0 | 0 | 0 | 0 |
5 | 0 | 0 | 0 | 0 | 0 |
6 | 0 | 0 | 0 | 0 | 0 |
7 | 2 | 0 | 0 | 0 | 0 |
8 | 0 | 0 | 0 | 0 | 0 |
9 | 2 | 0 | 0 | 0 | 0 |
10 | 0 | 0 | 0 | 0 | 0 |
11 | 35 | 3 | 1 | 0 | 0 |
12 | 0 | 0 | 0 | 0 | 0 |
13 | 153 | 6 | 2 | 0 | 0 |
14 | ? | 1 | 1 | 0 | 0 |
15 | ? | 149 | 25 | 0 | 0 |
16 | ? | 3 | 0 | 0 | 0 |
17 | ? | ? | 244 | 0 | 0 |
18 | ? | ? | 1 | 0 | 0 |
19 | ? | ? | 4129 | 4 | 0 |
20 | ? | ? | 3 | 1 | 0 |
21 | ? | ? | ? | 98 | 0 |
22 | ? | ? | ? | 0 | 0 |
23 | ? | ? | ? | 6036 | 0 |
24 | ? | ? | ? | 52 | 0 |
25 | ? | ? | ? | ? | 0 |
26 | ? | ? | ? | ? | 0 |
27 | ? | ? | ? | ? | 8 |
[1] J. Goedgebeur, K. Noguchi, J. Renders and C.T. Zamfirescu, HIST-Critical Graphs and Malkevitch’s Conjecture, manuscript.