Hamiltonicity of -traceable graphs.
Hamiltonsche Linien im Quadrat brückenloser Graphen mit Artikulationen.
Hamiltonwege in rechteckigen und quaderförmigen Gittergraphen.
Handcuffed Designs.
Handshakes across a (round) table.
Hankel determinants and the Sylvester theorem. (Déterminants de Hankel et théorème de Sylvester.)
Hankel determinants of some sequences of polynomials.
Harary Index of Product Graphs
The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, the exact formulae for the Harary indices of tensor product G × Km0,m1,...,mr−1 and the strong product G⊠Km0,m1,...,mr−1 , where Km0,m1,...,mr−1 is the complete multipartite graph with partite sets of sizes m0,m1, . . . ,mr−1 are obtained. Also upper bounds for the Harary indices of tensor and strong products of graphs are estabilished. Finally, the exact formula...
Hard squares with negative activity and rhombus tilings of the plane.
Hard squares with negative activity on cylinders with odd circumference.
Hardness of embedding simplicial complexes in
Let be the following algorithmic problem: Given a finite simplicial complex of dimension at most , does there exist a (piecewise linear) embedding of into ? Known results easily imply polynomiality of (; the case is graph planarity) and of for all . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that and are undecidable for each . Our main result is NP-hardness of and, more generally, of for all , with...
Hardness Results for Total Rainbow Connection of Graphs
A total-colored path is total rainbow if both its edges and internal vertices have distinct colors. The total rainbow connection number of a connected graph G, denoted by trc(G), is the smallest number of colors that are needed in a total-coloring of G in order to make G total rainbow connected, that is, any two vertices of G are connected by a total rainbow path. In this paper, we study the computational complexity of total rainbow connection of graphs. We show that deciding whether a given total-coloring...
Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products
The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras...
Harmonic functions and Hardy spaces on trees with boundaries
Harmonic functions on annuli of graphs
Harmonic functions on multiplicative graphs and interpolation polynomials.
Harmonic number identities via Euler's transform.
Hayman admissible functions in several variables.
Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs
Let G be a graph on n vertices. A vertex of G with degree at least n/2 is called a heavy vertex, and a cycle of G which contains all the heavy vertices of G is called a heavy cycle. In this note, we characterize graphs which contain no heavy cycles. For a given graph H, we say that G is H-heavy if every induced subgraph of G isomorphic to H contains two nonadjacent vertices with degree sum at least n. We find all the connected graphs S such that a 2-connected graph G being S-heavy implies any longest...
Heavy subgraph pairs for traceability of block-chains
A graph is called traceable if it contains a Hamilton path, i.e., a path containing all its vertices. Let G be a graph on n vertices. We say that an induced subgraph of G is o−1-heavy if it contains two nonadjacent vertices which satisfy an Ore-type degree condition for traceability, i.e., with degree sum at least n−1 in G. A block-chain is a graph whose block graph is a path, i.e., it is either a P1, P2, or a 2-connected graph, or a graph with at least one cut vertex and exactly two end-blocks....