CRN: 21139
MAD 6207 Combinatorics II, Spring 2012
MWF 2:00-2:50pm, PHY109
Assignment 1 suggested solutions
Note: All graphs are simple graphs. Questions 2, 3, 4 give (two) dierent methods for obtaining a
weakened form of Turns Theorem, while Q5 gives a st
CRN: 21139
MAD 6207 Combinatorics II, Spring 2012
MWF 2:00-2:50pm, PHY109
Assignment 3 suggested solutions
Question 1. (2 points) A perfect matching (or 1-factor) of a graph G is a matching in which every
vertex in G is matched. That is, a perfect matchin
CRN: 21139
MAD 6207 Combinatorics II, Spring 2012
MWF 2:00-2:50pm, PHY109
Assignment 2 suggested solutions
Question 1. (2 points) Let G = (V, E ) be a graph with n vertices, m edges and t copies of C4 . A
copy of C4 in G is a subgraph of G isomorphic to C
CRN: 21139
MAD 6207 Combinatorics II, Spring 2012
MWF 2:00-2:50pm, PHY109
Assignment 4 suggested solutions
Question 1. (1 point) (a) Find the 35th set in the the colex order of 4-subsets of [10].
(b) Find 60th set in the colex order of 5-subsets of [10].
CRN: 21139
MAD 6207 Combinatorics II, Spring 2012
MWF 2:00-2:50pm, PHY109
Assignment 5 suggested solutions
We say that (E, E ), where E 2E , is a matroid if
(I1) E ,
(I2) A B and B E imply that A E , and
(I3) A, B E and |A| < |B | imply that there is e B
CRN: 21139
MAD 6207 Combinatorics II, Spring 2012
MWF 2:00-2:50pm, PHY109
Assignment 8 suggested solutions
Question 1. (2 points) Let v be a prime power and suppose that v = 4t 1 for some integer t 2. Let
D1 be the set of all squares in Fv and D2 be the s
CRN: 21139
MAD 6207 Combinatorics II, Spring 2012
MWF 2:00-2:50pm, PHY109
Assignment 7 suggested solutions
Question 1. (1 point) Consider K6 , the complete graph on [6]. Take the edge set of K6 as P . The
blocks are all sets of 3 edges that either form a
CRN: 21139
MAD 6207 Combinatorics II, Spring 2012
MWF 2:00-2:50pm, PHY109
Assignment 6 suggested solutions
Question 1. (2 points) Let M = (E, E ) be a matroid with B as its set of bases and r as its rank
function. Assume X E , and dene
BM \X = cfw_B : B E