17 necessary and sufficient conditions for the primality of Fermat numbers
'3in1' enhanced: three squared ways to '3in1' GRAPHS
3-transitive digraphs
Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is 3-transitive if the existence of the directed path (u,v,w,x) of length 3 in D implies the existence of the arc (u,x) ∈ A(D). In this article strong 3-transitive digraphs are characterized and the structure of non-strong 3-transitive digraphs is described. The results are used, e.g., to characterize 3-transitive digraphs that are transitive and to characterize 3-transitive digraphs with...
4-Transitive Digraphs I: The Structure of Strong 4-Transitive Digraphs
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is transitive if for every three distinct vertices u, v,w ∈ V (D), (u, v), (v,w) ∈ A(D) implies that (u,w) ∈ A(D). This concept can be generalized as follows: A digraph is k-transitive if for every u, v ∈ V (D), the existence of a uv-directed path of length k in D implies that (u, v) ∈ A(D). A very useful structural characterization of transitive digraphs has been known for a long time, and...
A bound for the rank-one transient of inhomogeneous matrix products in special case
We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length are rank-one, as it was shown in [6] (Shue, Anderson, Dey 1998). We establish a bound on the transient after which any product of matrices whose length exceeds that bound becomes rank-one.
A characterization of a class of graphs connected with the hysteresis phenomena
A class of tight circulant tournaments
A tournament is said to be tight whenever every 3-colouring of its vertices using the 3 colours, leaves at least one cyclic triangle all whose vertices have different colours. In this paper, we extend the class of known tight circulant tournaments.
A combinatorial approach to the conditioning of a single entry in the stationary distribution for a Markov chain.
A conjecture on cycle-pancyclism in tournaments
Let T be a hamiltonian tournament with n vertices and γ a hamiltonian cycle of T. In previous works we introduced and studied the concept of cycle-pancyclism to capture the following question: What is the maximum intersection with γ of a cycle of length k? More precisely, for a cycle Cₖ of length k in T we denote , the number of arcs that γ and Cₖ have in common. Let and f(n,k) = minf(k,T,γ)|T is a hamiltonian tournament with n vertices, and γ a hamiltonian cycle of T. In previous papers we gave...
A deceptive fact about functions
The paper provides a proof of a combinatorial result which pertains to the characterization of the set of equations which are solvable in the composition monoid of all partial functions on an infinite set.
A density result for random sparse oriented graphs and its relation to a conjecture of Woodall.
A Digrapf Approach to the Edge-Reconstruction Conjecture
A digraph equation for homomorphic images.
A dual proof of the upper bound conjecture for convex polytopes.
A further application of matrix analysis to communication structure in oceanic anthropology
A new bound for the spectral radius of Brualdi-Li matrices
Let B2m denote the Brualdi-Li matrix of order 2m, and let ρ2m = ρ(B2m ) denote the spectral radius of the Brualdi-Li Matrix. Then [...] . where m > 2, e = 2.71828 · · · , [...] and [...] .
A note on arc-disjoint cycles in tournaments
We prove that every vertex v of a tournament T belongs to at least arc-disjoint cycles, where δ⁺(T) (or δ¯(T)) is the minimum out-degree (resp. minimum in-degree) of T, and (or ) is the out-degree (resp. in-degree) of v.
A note on chromatic number of direct product of graphs
A note on kernels and solutions in digraphs
For given nonnegative integers k,s an upper bound on the minimum number of vertices of a strongly connected digraph with exactly k kernels and s solutions is presented.
A note on removing a point of a strong digraph