We show that a graph G with n vertices is a q-tree if and only if its chromatic polynomial is P(G,A) = A(A -I)...(A -q + l ) ( As ) " -~ where n L q. The graphs which we consider here are finite, undirected, simple, and loopless. Let q be an integer L 1. The graphs called q-trees are defined by re
On zero-trees
✍ Scribed by Zoltán Füredi; D. J. Kleitman
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 544 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Consider an integer‐valued function on the edge‐set of the complete graph K~m+1~. The weight of an edge‐subset is defined to be the sum of the associated weights. It is proved that there exists a spanning tree with weight 0 modulo m.
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