We give an upper bound on the sum of squares of l-degrees in a k-uniform hypergraph in terms of l, k and the number of vertices and edges of the hypergraph, where a l-degree is the number of edges of the hypergraph containing a fixed l-element subset of ...

It is known that the incidence algebra of a finite poset is not strongly simply connected if and only if its quiver contains a crown. We give a combinatorial condition on crowns which, if satisfied, forces the incidence algebra to be simply connected. ...

Let P be a finite ordered set, and let J(P) be the distributive lattice of order ideals of P. The covering relations of J(P) are naturally associated with elements of P; in this way, each element of P defines an involution on the set J(P). Let Γ(P) be ...

We establish simple combinatorial descriptions of the radical and irreducible representations specifically for the descent algebra of a Coxeter group of type D over any field.

A graph G is called (k, d)^*-choosable if for every assignment L satisfying |L(v)| = k for all v ∈ V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. Let g(G) denote the girth of G ...

Let G be a K₄-minor free graph with maximum degree Δ. We prove that the chromatic number of the square of G is at most (i) Δ + 3 if 2 ≤ Δ ≤ 3; or (ii) [3Δ/2] + 1 if Δ ≥ 4. Examples are given to show the bounds can be attained.

Every 2-connected simple cubic graph of order n ≥ 6 has a cycle cover with at most [n/4] cycles. This bound is best possible.

The k-wheel W_k is the graph obtained as a join of a vertex and the cycle of length k. It is proved that a subdivided wheel G embeds isometrically into a hypercube if and only if G is the subdivision graph S(K₄) of K₄ or G is obtained from the wheel W_k (...

A graph is one-regular if its automorphism group acts freely and transitively on the set of its arcs. In this paper, an infinite family of cubic one-regular graphs with unsolvable automorphism groups is constructed.

Let G be a 2-connected graph. A subset D of V(G) is a 2-connected dominating set if every vertex of G has a neighbor in D and D induces a 2-connected subgraph. Let γ₂(G) denote the minimum size of a 2-connected dominating set of G. Let δ(G) be the ...

We give a classification of countable ultrahomogeneous antimatroids of convex dimension 2. Our proof relies on a unique realization result for finite antimatroids of convex dimension 2.

For a graph G, the P₂-path graph, P₂(G), has for vertices the set of all paths of length 2 in G. Two vertices are connected when their union is a path or a cycle of length 3. We present lower bounds on the edge-connectivity, λ(P₂(G)) of a connected ...

A (D;g)-cage is a graph having the minimum number of vertices, with degree set D and girth g. Denote by f(D;g) the number of vertices in a (D;g)-cage. In this paper it is shown that f({r,m}; 6) ≥ 2(rm - m + 1) for any 2 ≤ r < m, and f({r, m}; 6) = 2(rm -...

An analogue of the exponential generating function for derangement numbers in the symmetric group algebras is introduced. It leads to n mutually orthogonal idempotents in the group algebra of the symmetric group S_n, for all n. The corresponding ...

Beginning from any finite unary algebra with at least two fundamental operations, there is an infinite ascending chain of finite algebras that are alternately dualisable and non-dualisable. We obtain this result while characterising the finite algebras ...

In 1979, two constructions for making partitionable graphs were introduced in (by Chvátal et al. (Ann. Discrete Math. 21 (1984) 197)). The graphs produced by the second construction are called CGPW graphs. A near-factorization (A, B) of a finite group ...

BL-algebras were introduced by Hájek as algebraic structures of Basic Logic. The aim of this paper is to analyze the structure of finite BL-algebras. Extending the notion of ordinal sum, we characterize a class of finite BL-algebras, actually BL-comets. ...

We prove that no Suzuki group Sz(q) can act line-transitively on a non-trivial finite linear space.

Given two triangular embeddings f and f' of a complete graph K and given a bijection φ : V(K) → V(K), denote by M(φ) the set of faces (x, y, z) of f such that (φ(x), φ(y), φ(z)) is not a face of f'. The distance between f and f' is the minimal value of |...

We study finite graphs which are covered by the 1-skeleton of a building of type Ã_n and with an extremal spectral property: they are Ã_n-Ramanujan in the sense of Lubotzky. That definition is made quantitatively explicit, refined in the directed case, ...