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## Degree-preserving network growth

Real-world networks evolve over time through the addition or removal of nodes and edges. In current network-evolution models, the degree of each node varies or grows arbitrarily, yet there are many networks for which a different description is …

## The mixing time of switch Markov chains: a unified approach

We show that the switch Markov chain is rapidly mixing on $P$-stable degree sequences of simple, bipartite, and directed graphs. Consequently, we have rapid mixing on power-law distribution-bounded degree sequences with parameter $\gamma2$ and on …

## Half-graphs, other non-stable degree sequences, and the switch Markov chain

In this paper we give a non-trivial family of degree sequences that are not $P$-stable and the switch Markov chain is still rapidly mixing on them. This family has an intimate connection to Tyshkevich-decompositions and strong stability as well.

## Rooted NNI moves and distance-1 tail moves on tree-based phylogenetic networks

We show that the space of rooted tree-based phylogenetic networks is connected under rooted nearest-neighbour interchange (rNNI) moves and distance-1 tail moves.

## Computing the Difficulty of Critical Bootstrap Percolation Models is NP-hard

Bootstrap percolation is a class of cellular automata with random initial state. Two-dimensional bootstrap percolation models have three universality classes, the most studied being the 'critical' one. For this class the scaling of the quantity of …

## Efficiently sampling the realizations of bounded, irregular degree sequences of bipartite and directed graphs

Since 1997 a considerable effort has been spent on the study of the **swap** (switch) Markov chains on graphic degree sequences. All of these results assume some kind of regularity in the corresponding degree sequences. Recently, Greenhill and …

## Mobile vs. point guards

We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using "rectangular vision". We prove a sharp bound on the minimum number of point guards required to cover the gallery …

## Oral administration of pyrophosphate inhibits connective tissue calcification

Various disorders including pseudoxanthoma elasticum (PXE) and generalized arterial calcification of infancy (GACI), which are caused by inactivating mutations in *ABCC6* and *ENPP1*, respectively, present with extensive tissue calcification due to …

## Terminal-Pairability in Complete Bipartite Graphs with Non-Bipartite Demands

We investigate the terminal-pairability problem in the case when the base graph is a complete bipartite graph, and the demand graph is a (not necessarily bipartite) multigraph on the same vertex set. In computer science, this problem is known as the …

## Terminal-Pairability in Complete Bipartite Graphs

We investigate the terminal-pairability problem in the case when the base graph is a complete bipartite graph, and the demand graph is also bipartite with the same color classes. We improve the lower bound on maximum value of $\Delta(D)$ which still …