How can I calculate whether I can form a group of 10 tournament matches from a limited set of matches/pairs?

Question

I'm trying to work out whether I can form 10 matches from a set of 98 possible player pairings (which includes 20 individuals).

Each player must play in one, and only one, of the matches.

A computational approach is fine, but there are too many possibilities to enumerate---14005614014756, to be precise, i.e. choose(98, 10).

The data for the allowable match pairs is:

Player01 Player13 Player01 Player14 Player02 Player03 Player02 Player04 Player02 Player05 Player02 Player06 Player02 Player07 Player02 Player08 Player02 Player09 Player02 Player10 Player02 Player11 Player02 Player12 Player02 Player13 Player02 Player14 Player02 Player15 Player02 Player16 Player02 Player17 Player02 Player18 Player02 Player19 Player02 Player20 Player03 Player04 Player03 Player05 Player03 Player06 Player03 Player07 Player03 Player08 Player03 Player09 Player03 Player10 Player03 Player11 Player03 Player12 Player03 Player13 Player03 Player14 Player03 Player15 Player03 Player16 Player03 Player17 Player03 Player18 Player03 Player19 Player03 Player20 Player04 Player05 Player04 Player06 Player04 Player07 Player04 Player08 Player04 Player09 Player04 Player10 Player04 Player11 Player04 Player12 Player04 Player13 Player04 Player14 Player04 Player15 Player04 Player16 Player04 Player17 Player04 Player18 Player04 Player19 Player04 Player20 Player06 Player07 Player06 Player08 Player06 Player09 Player06 Player10 Player06 Player11 Player06 Player12 Player06 Player13 Player06 Player14 Player06 Player15 Player06 Player16 Player06 Player17 Player06 Player18 Player06 Player19 Player06 Player20 Player07 Player09 Player07 Player15 Player08 Player09 Player08 Player10 Player08 Player11 Player08 Player12 Player08 Player13 Player08 Player14 Player08 Player15 Player08 Player16 Player08 Player17 Player08 Player18 Player08 Player19 Player08 Player20 Player09 Player10 Player09 Player13 Player09 Player14 Player09 Player15 Player09 Player20 Player10 Player13 Player13 Player14 Player13 Player15 Player13 Player17 Player14 Player20 Player16 Player17 Player16 Player18 Player16 Player19 Player16 Player20 Player18 Player19 Player18 Player20 Player19 Player20

Answer 1

I was able to identify the existence of one using the blossom algorithm.