منابع مشابه
Toida's Conjecture is True
Let S be a subset of the units in Zn. Let Γ be a circulant graph of order n (a Cayley graph of Zn) such that if ij ∈ E(Γ), then i − j (mod n) ∈ S. Toida conjectured that if Γ′ is another circulant graph of order n, then Γ and Γ′ are isomorphic if and only if they are isomorphic by a group automorphism of Zn. In this paper, we prove that Toida’s conjecture is true. We further prove that Toida’s ...
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In 1958 Lax conjectured that hyperbolic polynomials in three variables are determinants of linear combinations of three symmetric matrices. This conjecture is equivalent to a recent observation of Helton and Vinnikov. Consider a polynomial p on R of degree d (the maximum of the degrees of the monomials in the expansion of p). We call p homogeneous if p(tw) = tp(w) for all real t and vectors w ∈...
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In 1977 a five-part conjecturewasmade about a family of groups related to trivalent graphs and one part of the conjecture was proved. The conjecture completely determines all finite members of the family. Here we prove another part of the conjecture and foreshadow a paper which completes the proof of the other three parts.
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In the 70s, Goldberg, and independently Seymour, conjectured that for any multigraph G, the chromatic index χ′(G) satisfies χ′(G) ≤ max{∆(G) + 1, dρ(G)e}, where ρ(G) = max{ e(G[S]) b|S|/2c | S ⊆ V }. We show that their conjecture (in a stronger form) is true for random multigraphs. Let M(n,m) be the probability space consisting of all loopless multigraphs with n vertices and m edges, in which m...
متن کاملThe Prime Power Conjecture is True for
The Prime Power Conjecture (PPC) states that abelian planar difference sets of order n exist only for n a prime power. Evans and Mann [1] verified this for cyclic difference sets for n ≤ 1600. In this paper we use the Mann test to verify the PPC for n ≤ 2, 000, 000.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2002
ISSN: 1077-8926
DOI: 10.37236/1651