Homomorphisms of infinite bipartite graphs onto complete bipartite graphs
Homomorphisms of triangle groups with large injectivity radius.
Homopolar circuits in polar graphs
Homotopy and homology in pretopological spaces
Homotopy equivalence of isospectral graphs.
Hook length formulas for trees by Han's expansion.
Horocyclic products of trees
Let be homogeneous trees with degrees , respectively. For each tree, let be the Busemann function with respect to a fixed boundary point (end). Its level sets are the horocycles. The horocyclic product of is the graph consisting of all -tuples with , equipped with a natural neighbourhood relation. In the present paper, we explore the geometric, algebraic, analytic and probabilistic properties of these graphs and their isometry groups. If and then we obtain a Cayley graph of the...
Hosoya polynomial of Hanoi graphs
How frequently is a system of 2-linear Boolean equations solvable?
How Long Can One Bluff in the Domination Game?
The domination game is played on an arbitrary graph G by two players, Dominator and Staller. The game is called Game 1 when Dominator starts it, and Game 2 otherwise. In this paper bluff graphs are introduced as the graphs in which every vertex is an optimal start vertex in Game 1 as well as in Game 2. It is proved that every minus graph (a graph in which Game 2 finishes faster than Game 1) is a bluff graph. A non-trivial infinite family of minus (and hence bluff) graphs is established. minus graphs...
How the result of graph clustering methods depends on the construction of the graph
We study the scenario of graph-based clustering algorithms such as spectral clustering. Given a set of data points, one first has to construct a graph on the data points and then apply a graph clustering algorithm to find a suitable partition of the graph. Our main question is if and how the construction of the graph (choice of the graph, choice of parameters, choice of weights) influences the outcome of the final clustering result. To this end we study the convergence of cluster quality measures...
How to draw tropical planes.
How to find overfull subgraphs in graphs with large maximum degree. II.
Hyperbolic and Parabolic Packings.
Hyperbolicity and chordality of a graph.
Hyperconvexity of ℝ-trees
It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.
Hyperelliptic maps and surfaces
Hyperenergetic and Hypoenergetic Graphs
Hyperenergetic graphs and cyclomatic number
Hypergraph systems and their extensions