**Combinatorial and Discrete Geometry: Sheet P**

Prepared by:

Joseph Malkevitch

Department of Mathematics and Computer Studies

York College (CUNY)

Jamaica, New York 11451

email: joeyc@cunyvm.cuny.edu

web page: http://www.york.cuny.edu/~malk

1. Find a system of distinct representatives, if possible, for the set systems below. If there is no SDR, find a "partial" system of distinct representatives that is as large as possible.

(i)

a = {x, y, z, w, u, v}

b = {x, u, v}

c = {y, u, v}

d = {z, u, v}

e = {x, y, z}

f = {x, w, u v}

(ii)

a = {x, y, z, u, v, w, s}

b = {s, u}

c = {s, v, y}

d = { y, z, u}

e = {v}

f = {y, z}

g = {s. w. z}