Superperfect pairs of trees in graphs
β Scribed by Ladislav A. Novak; Alan Gibbons
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 414 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0098-9886
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## Abstract A multicolored tree is a tree whose edges have different colors. Brualdi and Hollingsworth 5 proved in any proper edge coloring of the complete graph __K__~2__n__~(__n__ > 2) with 2__n__ β 1 colors, there are two edgeβdisjoint multicolored spanning trees. In this paper we generalize thi
We prove the existence of two edge-disjoint multicolored spanning trees in any edge-coloring of a complete graph by perfect matchings; we conjecture that a full partition into multicolored spanning trees is always possible.
In a graph G Γ (V, E) if we think of each vertex s as the possible location for a guard capable of protecting each vertex in its closed neighborhood N[s], then ''domination'' requires every vertex to be protected. Thus, S Κ V (G) is a dominating set if Κ s β S N[s] Γ V (G). For total domination, eac