A note on the Erdos-Faber-Lovasz Conjecture: quasigroups and complete digraphs
Por:
Araujo-Pardo, G., Rubio-Montiel, C., Vazquez-Avila, A.
Publicada:
1 ene 2019
Categoría:
Mathematics (miscellaneous)
Resumen:
A decomposition of a simple graph G is a pair (G, P) where P is a set of
subgraphs of G, which partitions the edges of G in the sense that every
edge of G belongs to exactly one subgraph in P. If the elements of P are
induced subgraphs then the decomposition is denoted by [G, P].
A k-P- coloring of a decomposition (G, P) is a surjective function that
assigns to the edges of G a color from a k-set of colors, such that all
edges of H is an element of P have the same color, and, if H-1, H-2 is
an element of P with V(H-1)boolean AND V(H-2) not equal 0 then E(H-1)
and E(H-2) have different colors. The chromatic index x' ((G, P)) of a
decomposition (G, P) is the smallest number k for which there exists a
k-P-coloring of (G, P).
The well-known Erdos-Faber-Lovasz Conjecture states that any
decomposition [K-n, P] satisfies x' ([K-n, P]) <= n. We use
quasigroups and complete digraphs to give a new family of decompositions
that satisfy the conjecture.
Filiaciones:
Araujo-Pardo, G.:
Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico
Rubio-Montiel, C.:
Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico
Comenius Univ, Dept Algebra, Bratislava 84248, Slovakia
Vazquez-Avila, A.:
Univ Aeronaut Queretaro, Subdirecc Ingn & Posgrad, Queretaro 76270, Mexico
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