AMS
301.1
First
Test,
Fall
2009,
SOLUTIONS
1.
Graphs
are
isomorphic.See
Figure
1.19
in
text.
2. Test A: LB = 18 (subtracting first from rows). Don't use (1,3), LB=22; use (1.3) (deleting row 1
&
col
3
and
setting
(entry
(3,1)
=
infinity),
LB
=
19.
Test B: LB = 14 (subtracting first from rows). Don't use (1,3), LB = 19; use (1,3) (deleting row 1
col
3
and
setting
entru
(3,1)
=
infinity),
LB=
16
3.
Test
A:
connected;
test
B:
not
connected
4. Test A and 5. Test B: vertices equal actuaries/statisticians, edges = personaly conflicts, colors =
hotels;
does
6
colors
suffice?
5. Test A and 4. Test B: a) not possible, violates e <=3v-6; b) possible, v = (Test A, 12), (Test B,
10)-- remember that all vertices musst have deg 3; c) many possibilities, e.g., triangle with trailing
path
(like
a
kite),
6. As explained in class, by symmetry and need to use at least one vertical edge, you can assume
you start with edge (c,h), at c by symmetry choose b-c & delete c-d, forcing at d, e-d-i. Two cases
at