Decompositions into isomorphic rainbow spanning trees

Trees with Α-labelings and decompositions of complete graphs into non-symmetric isomorphic spanning trees

We examine constructions of non-symmetric trees with a flexible q-labeling or an α-like labeling, which allow factorization of K2n into spanning trees, arising from the trees with α-labelings.

Bi-cyclic decompositions of complete graphs into spanning trees

We examine decompositions of complete graphs with an even number of vertices, K2n, into n isomorphic spanning trees. While methods of such decompositions into symmetric trees have been known, we develop here a more general method based on a new type of vertex labelling, called flexible q-labelling. This labelling is a generalization of labellings introduced by Rosa and Eldergill.

Multicolored Isomorphic Spanning Trees in Complete Graphs

In this paper, we first prove that if the edges of K2m are properly colored by 2m− 1 colors in such a way that any two colors induce a 2-factor of which each component is a 4-cycle, then K2m can be decomposed into m isomorphic multicolored spanning trees. Consequently, we show that there exist three disjoint isomorphic multicolored spanning trees in any properly (2m−1)-edge-colored K2m for m ≥ 14.

Multicolored Parallelisms of Isomorphic Spanning Trees

A subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors. In this paper, we prove that a complete graph on 2m (m = 2) vertices K2m can be properly edge-colored with 2m − 1 colors in such a way that the edges of K2m can be partitioned into m multicolored isomorphic spanning trees.

Minimal Decompositions of Hypergraphs into Mutually Isomorphic Subhypergraphs