Minimal size of a graph with diameter 2 and given maximal degree. II.
Minimal trees and monophonic convexity
Let V be a finite set and 𝓜 a collection of subsets of V. Then 𝓜 is an alignment of V if and only if 𝓜 is closed under taking intersections and contains both V and the empty set. If 𝓜 is an alignment of V, then the elements of 𝓜 are called convex sets and the pair (V,𝓜 ) is called an alignment or a convexity. If S ⊆ V, then the convex hull of S is the smallest convex set that contains S. Suppose X ∈ ℳ. Then x ∈ X is an extreme point for X if X∖{x} ∈ ℳ. A convex geometry on a finite set is...
Minimal vertex degree sum of a 3-path in plane maps
Let wₖ be the minimum degree sum of a path on k vertices in a graph. We prove for normal plane maps that: (1) if w₂ = 6, then w₃ may be arbitrarily big, (2) if w₂ < 6, then either w₃ ≤ 18 or there is a ≤ 15-vertex adjacent to two 3-vertices, and (3) if w₂ < 7, then w₃ ≤ 17.
Minimale nicht in die Ringfläche einbettbare Graphen.
Minimal-Energy Clusters of Hard Spheres.
Minimally n-line connected graphs.
Minimax degrees of quasiplane graphs without 4-faces.
Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth
In this paper we consider the following problem: Over the class of all simple connected unicyclic graphs on vertices with girth (, being fixed), which graph minimizes the Laplacian spectral radius? Let be the lollipop graph obtained by appending a pendent vertex of a path on
Minimum congestion spanning trees of grids and discrete toruses
The paper is devoted to estimates of the spanning tree congestion for grid graphs and discrete toruses of dimensions two and three.
Minimum connected dominating sets of random cubic graphs.
Minimum convex-cost tension problems on series-parallel graphs
We present briefly some results we obtained with known methods to solve minimum cost tension problems, comparing their performance on non-specific graphs and on series-parallel graphs. These graphs are shown to be of interest to approximate many tension problems, like synchronization in hypermedia documents. We propose a new aggregation method to solve the minimum convex piecewise linear cost tension problem on series-parallel graphs in operations.
Minimum convex-cost tension problems on series-parallel graphs
We present briefly some results we obtained with known methods to solve minimum cost tension problems, comparing their performance on non-specific graphs and on series-parallel graphs. These graphs are shown to be of interest to approximate many tension problems, like synchronization in hypermedia documents. We propose a new aggregation method to solve the minimum convex piecewise linear cost tension problem on series-parallel graphs in O(m3) operations.
Minimum cut in directed planar networks
Minimum degree, leaf number and traceability
Let be a finite connected graph with minimum degree . The leaf number of is defined as the maximum number of leaf vertices contained in a spanning tree of . We prove that if , then is 2-connected. Further, we deduce, for graphs of girth greater than 4, that if , then contains a spanning path. This provides a partial solution to a conjecture of the computer program Graffiti.pc [DeLaVi na and Waller, Spanning trees with many leaves and average distance, Electron. J. Combin. 15 (2008),...
Minimum distances of error-correcting codes in incidence rings.
Minimum functors on categories of Neumann trees
Minimum maximal graphs with forbidden subgraphs
Minimum rank of a tree over an arbitrary field.
Minimum rank of edge subdivisions of graphs.
Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers.