Discrete Mathematics

Let G be a bipartite graph with bipartition (X,Y) which has a perfect matching. It is proved that G is n-extendable if and only if for any perfect matching M of G and for each pair of vertices x in X and y in Y there are n internally disjoint M-...

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 ...

In this paper we prove two multiset analogs of classical results. We prove a multiset analog of Lovász's version of the Kruskal-Katona Theorem and an analog of the Bollobás-Thomason threshold result. As a corollary we obtain the existence of pebbling ...

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, ...

The set of trees with n vertices and the set of trees with perfect matchings are denoted by F_n, and T_2k, respectively. M. Hofmeister determined the first five maximum value of the largest eigenvalue of trees in F_n and gave the corresponding trees (...

For a coloring c of a connected graph G, let Π = (C₁, C₂, ..., C_k) be an ordered partition of V(G) into the resulting color classes. For a vertex v of G, the color code c_Π(v) of v is the ordered k-tuple (d(v, C₁), d(v, C₂),..., d(v, C_k)), where d(v, C_i) ...

We present an O(n²) order algorithm to an n-Tokyoites' loop-line commuter problem. The n-Tokyoites' loop-line commuter problem comprises a special class of the more general Gilmore-Gomory weighted bipartite matching problem where weights assigned to ...

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 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 positive integers j ≥ k, an L(j, k)-labeling of graph G is an integer labeling of V(G) such that adjacent vertices receive labels which differ by at least j, and vertices that are distance two apart receive labels which differ by at least k. The λ_{j, ...}

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 |...

In 1978, Murty and Simon asked the following question: when can the rank function of a polymatroid be decomposed as the sum of rank functions of matroids? Another natural question to ask is the following: when is this decomposition unique? In this paper,...

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

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 ...

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 ...

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 ...

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 -...

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 ...

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 ...

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 ...

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.

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 (...

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.

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.

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 ...

The relationship between the isoperimetric constants of a connected finite graph and the first positive eigenvalues of discrete Laplacians is studied. Two improvements of the well-known Cheeger inequalities of a graph are given.

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.

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. ...