A majority coloring of a directed graph is vertex-coloring in which every vertex has the same color as at most half its out-neighbors. Kreutzer, Oum, Seymour, van der Zypen and Wood proved that digraph $4$-coloring conjectured admits $3$-coloring. They observed Local Lemma implies conjecture for digraphs large enough minimum out-degree if, crucially, maximum in-degree bounded by a(n exponential...

We propose the notion of a majority $k$-edge-coloring graph $G$, which is an edge-coloring $G$ with $k$ colors such that, for every vertex $u$ at most half edges incident have same color. show best possible results that minimum degree least $2$ has $4$-edge-coloring, and $4$ $3$-edge-coloring. Furthermore, we discuss natural variation edge-colorings some related open problems.

Abstract We study finite-time bit erasure in the context of majority-logic decoding. In particular, we calculate minimum amount work needed to erase a when one has full control over system dynamics. show that although single unit is easier slow-driving limit, general outperforms fast-erasure limit. Our results also suggest optimal design principles for bits under limited control.

We shall consider the discrete time synchronous random majority-vote cellular automata on the n by n torus, in which every vertex is in one of two states and, at each time step t, every vertex goes into the state the majority of its neighbours had at time t−1 with a small chance p of error independently of all other events. We shall show that, if n is fixed and p is sufficiently small, then the...

Since the delineation of 12 bacterial phyla by comparative phylogenetic analyses of 16S ribosomal RNA in 1987 knowledge of microbial diversity has expanded dramatically owing to the sequencing of ribosomal RNA genes cloned from environmental DNA. Currently, only 26 of the approximately 52 identifiable major lineages, or phyla, within the domain Bacteria have cultivated representatives. Evidence...

The present study investigates the social-cognitive underpinnings of young children's bias to follow majority. More specifically, we focus on question whether children not only copy behavior a majority peers, but they also understand this as social norm that everyone needs follow. Additionally, investigated seeing unanimous or and dissenting peer makes difference for normative understanding. Pa...

We study a model in which a group of agents make a sequence of collective decisions on whether to remain in the current state of the system or switch to an alternative state, as proposed by one of them. Examples for instantiations of this model include the step-wise refinement of a bill of law by means of amendments to be voted on, as well as resource allocation problems, where agents successiv...

A majority coloring of a digraph is a coloring of its vertices such that for each vertex v, at most half of the out-neighbors of v have the same color as v. A digraph D is majority k-choosable if for any assignment of lists of colors of size k to the vertices there is a majority coloring of D from these lists. We prove that every digraph is majority 4-choosable. This gives a positive answer to ...

The number of prokaryotes and the total amount of their cellular carbon on earth are estimated to be 4-6 x 10(30) cells and 350-550 Pg of C (1 Pg = 10(15) g), respectively. Thus, the total amount of prokaryotic carbon is 60-100% of the estimated total carbon in plants, and inclusion of prokaryotic carbon in global models will almost double estimates of the amount of carbon stored in living orga...

Most supertree methods proposed to date are essentially ad hoc, rather than designed with particular properties in mind. Although the supertree problem remains difficult, one promising avenue is to develop from better understood consensus methods to the more general supertree setting. Here, we generalize the widely used majority-rule consensus method to the supertree setting. The majority-rule ...