Minimum degree and minimum number of edge-disjoint trees
نویسندگان
چکیده
منابع مشابه
Edge-Disjoint Induced Subgraphs with Given Minimum Degree
Let h be a given positive integer. For a graph with n vertices and m edges, what is the maximum number of pairwise edge-disjoint induced subgraphs, each having minimum degree at least h? There are examples for which this number is O(m2/n2). We prove that this bound is achievable for all graphs with polynomially many edges. For all > 0, if m > n1+ , then there are always Ω(m2/n2) pairwise edge-d...
متن کاملEdge-Disjoint Cliques in Graphs with High Minimum Degree
For a graph G and a fixed integer k ≥ 3, let νk(G) denote the maximum number of pairwise edge-disjoint copies of Kk in G. For a constant c, let η(k, c) be the infimum over all constants γ such that any graph G of order n and minimum degree at least cn has νk(G) ≥ γn2(1 − on(1)). By Turán’s Theorem, η(k, c) = 0 if c ≤ 1− 1/(k− 1) and by Wilson’s Theorem, η(k, c) → 1/(k2 − k) as c → 1. We prove t...
متن کاملLow-Degree Minimum Spanning Trees
Motivated by practical VLSI routing applications, we study the maximum vertex degree of a minimum spanning tree (MST). We prove that under the Lp norm, the maximum vertex degree over all MSTs is equal to the Hadwiger number of the corresponding unit ball; we show an even tighter bound for MSTs where the maximum degree is minimized. We give the best-known bounds for the maximum MST degree for ar...
متن کاملDegree-bounded minimum spanning trees
* to be exact, times the weight of a minimum spanning tree (MST). In particular, we present an improved analysis of Chan’s degree-4 MST algorithm [4]. Previous results. Arora [1] and Mitchell [9] presented PTASs for TSP in Euclidean metric, for fixed dimensions. Unfortunately, neither algorithm extends to find degree-3 or degree-4 trees. Recently, Arora and Chang [3] have devised a quasi-polyno...
متن کاملGirth, minimum degree, independence, and broadcast independence
An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(03)00108-0