More Examples and Counterexamples for a Conjecture of Merrifield and Simmons
More flexible radial layout.
More forbidden minors for wye-delta-wye reducibility.
More lr saturated L∞ spaces
2000 Mathematics Subject Classification: 05D10, 46B03.Given r ∈ (1, ∞), we construct a new L∞ separable Banach space which is lr saturated.
More monotonicity theorems for partitions.
More on betweenness-uniform graphs
We study graphs whose vertices possess the same value of betweenness centrality (which is defined as the sum of relative numbers of shortest paths passing through a given vertex). Extending previously known results of S. Gago, J. Hurajová, T. Madaras (2013), we show that, apart of cycles, such graphs cannot contain 2-valent vertices and, moreover, are 3-connected if their diameter is 2. In addition, we prove that the betweenness uniformity is satisfied in a wide graph family of semi-symmetric graphs,...
More on even [a,b]-factors in graphs
In this note we give a characterization of the complete bipartite graphs which have an even (odd) [a,b]-factor. For general graphs we prove that an a-edge connected graph G with n vertices and with δ(G) ≥ max{a+1,an/(a+b) + a - 2} has an even [a,b]-factor, where a and b are even and 2 ≤ a ≤ b. With regard to the edge-connectivity this result is slightly better than one of the similar results obtained by Kouider and Vestergaard in 2004 and unlike their results, this result has no restriction on the...
More on k-Sets of Finite Sets in the Plane.
More on the girth of graphs on Weyl groups
The girth of graphs on Weyl groups, with no restriction on the associated root system, is determined. It is shown that the girth, when it is defined, is 3 except for at most four graphs for which it does not exceed 4.
More on the Kechris-Pestov-Todorcevic correspondence: Precompact expansions
In 2005, the paper [KPT05] by Kechris, Pestov and Todorcevic provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow. This immediately led to an explicit representation of this invariant in many concrete cases. However, in some particular situations, the framework of [KPT05] does not allow one to perform the computation directly, but only after a slight modification of the original argument. The purpose of the present paper is to supplement [KPT05]...
More statistics on permutation pairs.
Morphing planar graph drawings with bent edges.
Morse-Bott functions with two critical values on a surface
We study Morse-Bott functions with two critical values (equivalently, nonconstant without saddles) on closed surfaces. We show that only four surfaces admit such functions (though in higher dimensions, we construct many such manifolds, e.g. as fiber bundles over already constructed manifolds with the same property). We study properties of such functions. Namely, their Reeb graphs are path or cycle graphs; any path graph, and any cycle graph with an even number of vertices, is isomorphic to the Reeb...
Motion planning in cartesian product graphs
Let G be an undirected graph with n vertices. Assume that a robot is placed on a vertex and n − 2 obstacles are placed on the other vertices. A vertex on which neither a robot nor an obstacle is placed is said to have a hole. Consider a single player game in which a robot or obstacle can be moved to adjacent vertex if it has a hole. The objective is to take the robot to a fixed destination vertex using minimum number of moves. In general, it is not necessary that the robot will take a shortest path...
Mots infinis
Motzkin numbers, central trinomial coefficients and hybrid polynomials.
Motzkin numbers of higher rank: generating function and explicit expression.
Motzkin paths and powers of continued fractions.
Motzkin paths and reduced decompositions for permutations with forbidden patterns.
Moufang trees and generalized quadrangles.