Research Article

Infinitely Many Trees with Maximum Number of Holes Zero, One, and Two

Table 4

Trees connectable for a vertex colored in a one-hole tree with hole .

Color of vertexConnectable treesCondition

and all colors less than adjacent to .
For , and all colors less than adjacent to .
or
and all colors greater than less than adjacent to .
and or and
and
, and all colors greater than less than adjacent to .
and all colors greater than less than adjacent to .

and all colors less than adjacent to .
For , and all colors less than adjacent to .
and all colors greater than less than adjacent to and .
or
or and
and all colors greater than less than adjacent to .
, and all colors greater than less than adjacent to .