In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has at least one vertex of degree at most k: that is, some vertex in the subgraph touches k or fewer of the subgraph's edges. The degeneracy of a graph is …

一个 算子，在一定条件下，作用于任何元素时都得到0，也可以叫退化。 总之，是一个东西的功能变弱了，就叫退化。 首先，需要说明一下，线性规划中的 退化解 并不是一个几何特征，因为解的退化与否与约束的定义形式有关。 （这里可以参考 退化与否与约束定义形式有关，但标准型的退化性能够保持。 如果要想从几何的角度看退化解，上面那篇叙述了一个例子。 二维空间中退化解位于三条或三条以上的线的交点，三维空间中退化解位于四个或四个以上的面的交。 如下图 …

2024年5月1日 · In this paper logarithms are binary. For an integer k, a graph G is said to be k-degenerate if every subgraph of G has a vertex of degree at most k. The minimum k such that G is k-degenerate is called the degeneracy of G. Bounded degeneracy forms a very general notion of graph sparsity that includes classes of bounded treewidth, planar graphs ...

We prove that for every constant M there is a graph with minimum degree M which is spectrally 50-degenerate. This settles a problem of Dvorak and Mohar. The spectral radius (G) of a ( nite, simple) graph G is the largest eigenvalue of its adjacency matrix. A graph is d-degenerate if any subgraph of it contains a vertex of degree at most d.

2022年11月14日 · Gallai's path decomposition conjecture states that if G is a connected graph on n vertices, then the edges of G can be decomposed into at most ⌈n 2⌉ paths. A graph is said to be an odd semi-clique if it can be obtained from a clique on 2k …

In this paper, we study the path decomposition in 2-degenerate graphs. The class of 2-degenerate graphs properly include outer-planar graphs, series-parallel graphs and planar graphs of girth at least 5 as subclasses. We prove that: Theorem 1. Let G …

A path is a walk in which all vertices and edges are distinct. The number of edges in a path P is called its length and is denoted as |P|. The notation v iPv j denotes the subpath of the path P starting at the vertex v i and ending at the vertex v j. For a path P and an edge xy /∈ P and xy incident on one of the endpoints of P, P ∪ xy ...

2015年5月25日 · Ramsey numbers of degenerate graphs By Choongbum Lee Abstract A graph is d-degenerate if all its subgraphs have a vertex of degree at most d. We prove that there exists a constant c such that for all natural numbers d and r, every d-degenerate graph H of chromatic number r with jV (H)j 2d22cr has Ramsey number at most 2d2cr jV (H)j. This solves a

2016年1月1日 · Degeneracy graphs have been applied to help solve the neighborhood problem, to explain why cycling in LP occurs, to develop algorithms to determine two-sided shadow prices, to determine all vertices of a (degenerate) convex polyhedron, and to perform sensitivity analysis under (primal) degeneracy.

Geometry of degeneracy (bottom of pg 106) From the example: degeneracy in 2 -dimension is represented by having more than two lines intersecting at an extreme point. = ) there is a redundant constraint. In general: degeneracy in d -dimension is represented by having more than d hyperplanes intersecting at an extreme point.