Decompositions of Graphs |
Contents
Hamiltonian Decompositions | 9 |
The Product of Three Cycles | 13 |
General Results | 28 |
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Common terms and phrases
an+1 an+2 an+3 B₂ bipartite graph block C3 x C3 cartesian product cells choose Cn x Cr coloring of G column complete bipartite graph complete graph completes the proof component coloring connected acyclic partition connected graph contain cubic graphs cut-vertex cycles in G decomposed denote disjoint distinct edge-coloring edges of G endpoints entry follows form a partition G G G G₂ graph G graph of order H₁ H₂ hypothesis on G indicates the coloring integer Kn,n Kn₂ Kronecker product Latin squares least Lemma Let G minimum number multiple edges n/2 sets number of hamiltonian ordered pair orthogonal pair of colors pairs to contradict partition for G red blue result S₂ satisfies Property shows similarly skew chromatic index skew edge coloring skew Room square Subcase subgraph Theorem three hamiltonian cycles tonian U₁ unordered pairs upper bound V₁ V₂ vertex W. T. Tutte ոլ ոշ սլ