A MAXIMAL SPANNING TREE
by Ross Eckler
Word Ways, 1994
The five-letter word network given below is partitioned into 27 subnetworks, each having a unique vowel-consonant pattern (Y in first position is deemed a consonant, otherwise a vowel). All words are in the Official Scrabble Players Dictionary: each subnetwork lists the total OSPD words in it. The network is a tree; there are no closed cycles. Since two subnetworks (one with CRWTH and PHPHT, the other with SCHMO and SCHWA) are unlinkable with the others, and three (vvvvv, vvvvc, vvvcv) are empty, the 27 that remain comprise a maximal spanning tree. A computer could be used to construct a tree with fewer total words.
100payer---14payee layer 1116curse--231curie | curve | 3ankhs | curvy | | 2101later 871curls-----curly 12ourie | mater carls 268ankes mates marls---19earls---13early antes mares-----marts anted mires tarts acted sires torts--647toots acred---66aired-----sired boots--296booty ached | boors ashed | 11chiao doors ashes 48shred | doers asses 58atria shrew 1430chino dyers arses | strew | | arsis | strep | | arris 11stria-----strip 874chink 6eyers arras strop think | | thank | | shank-slank-slant--183alant 110arias 420stoop shark | areas scoop shirk 192alane | scoot shirt aline | shoot-----short amine 4areae amide abide abode anode 42angle-----anole