A theorem for an axiomatic approach to metric properties of graphs
A theorem of O'Nan for finite linear spaces
A theorem on -connected graphs
A theorem on chains of finite sets, II
A theorem on Hamiltonian line graphs
A Tight Bound on the Set Chromatic Number
We provide a tight bound on the set chromatic number of a graph in terms of its chromatic number. Namely, for all graphs G, we show that χs(G) > ⌈log2 χ(G)⌉ + 1, where χs(G) and χ(G) are the set chromatic number and the chromatic number of G, respectively. This answers in the affirmative a conjecture of Gera, Okamoto, Rasmussen and Zhang.
A topology with order, graph and an enumeration problem.
A tournament result deduced from harems.
A traceability conjecture for oriented graphs.
A transvection decomposition in GL(n,2)
An algorithm is given to decompose an automorphism of a finite vector space over ℤ₂ into a product of transvections. The procedure uses partitions of the indexing set of a redundant base. With respect to tents, i.e. finite ℤ₂-representations generated by a redundant base, this is a decomposition into base changes.
A tree as a finite nonempty set with a binary operation
A (finite) acyclic connected graph is called a tree. Let be a finite nonempty set, and let be the set of all trees with the property that is the vertex set of . We will find a one-to-one correspondence between and the set of all binary operations on which satisfy a certain set of three axioms (stated in this note).
A triangle free configuration
A triple lacunary generating function for Hermite polynomials.
A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs
A graph G on n vertices is said to be pancyclic if it contains cycles of all lengths k for k ∈ {3, . . . , n}. A vertex v ∈ V (G) is called super-heavy if the number of its neighbours in G is at least (n+1)/2. For a given graph H we say that G is H-f1-heavy if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K), dK(u, v) = 2 implies that at least one of them is super-heavy. For a family of graphs H we say that G is H-f1-heavy, if G is H-f1-heavy for every graph...
A Turán type problem concerning the powers of the degrees of a graph.
A two parameter chromatic symmetric function.
A two-dimensional pictorial presentation of Berele's insertion algorithm for symplectic tableaux.
A unified approach to the study of general and palindromic compositions.
A Unified Approach to Visibility Representations of Planar Graphs.
A unified construction of finite geometries associated with -clans in characteristic 2.