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Majority choosability of 1-planar digraph

Weihao Xia, Jihui Wang, Jiansheng Cai (2023)

Czechoslovak Mathematical Journal

A majority coloring of a digraph D with k colors is an assignment π : V ( D ) { 1 , 2 , , k } such that for every v V ( D ) we have π ( w ) = π ( v ) for at most half of all out-neighbors w N + ( 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 if U ( D ) is a 1-planar graph without a 4-cycle, then D is majority 3-choosable. And we also prove that every NIC-planar digraph is majority 3-choosable.

Mapping directed networks.

Crofts, Jonathan J., Estrada, Ernesto, Higham, Desmond J., Taylor, Alan (2010)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Marginalization in models generated by compositional expressions

Francesco M. Malvestuto (2015)

Kybernetika

In the framework of models generated by compositional expressions, we solve two topical marginalization problems (namely, the single-marginal problem and the marginal-representation problem) that were solved only for the special class of the so-called “canonical expressions”. We also show that the two problems can be solved “from scratch” with preliminary symbolic computation.

Markov convexity and local rigidity of distorted metrics

Manor Mendel, Assaf Naor (2013)

Journal of the European Mathematical Society

It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type p if and only if it is Markov p -convex. Counterexamples are constructed to natural questions related to isomorphic uniform convexity of metric spaces, showing in particular that tree metrics fail to have the dichotomy property.

Matchings and total domination subdivision number in graphs with few induced 4-cycles

Odile Favaron, Hossein Karami, Rana Khoeilar, Seyed Mahmoud Sheikholeslami (2010)

Discussiones Mathematicae Graph Theory

A set S of vertices of a graph G = (V,E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γₜ(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number s d γ ( G ) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. Favaron, Karami, Khoeilar and Sheikholeslami (Journal of Combinatorial...

Matchings in complete bipartite graphs and the r -Lah numbers

Gábor Nyul, Gabriella Rácz (2021)

Czechoslovak Mathematical Journal

We give a graph theoretic interpretation of r -Lah numbers, namely, we show that the r -Lah number n k r counting the number of r -partitions of an ( n + r ) -element set into k + r ordered blocks is just equal to the number of matchings consisting of n - k edges in the complete bipartite graph with partite sets of cardinality n and n + 2 r - 1 ( 0 k n , r 1 ). We present five independent proofs including a direct, bijective one. Finally, we close our work with a similar result for r -Stirling numbers of the second kind.

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