منابع مشابه
Minimum Degree and Dominating Paths
A dominating path in a graph is a path P such that every vertex outside P has a neighbor on P. A result of Broersma from 1988 implies that if G is an n-vertex k-connected graph and δ(G) > n−k k+2 − 1, then G contains a dominating path. We prove the following results. The lengths of dominating paths include all values from the shortest up to at least min{n − 1,2δ(G)}. For δ(G) > an, where a is a...
متن کاملDegree Sum and Vertex Dominating Paths
A vertex dominating path in a graph is a path P such that every vertex outside P has a neighbor on P . In 1988 H. Broersma stated a result implying that every n-vertex kconnected graph G such that σ(k+2)(G) ≥ n− 2k − 1 contains a dominating path. We show that every n-vertex k-connected graph with σ2(G) ≥ 2n k+2 + f(k) contains a dominating path of length at most O(|T |), where T is a minimum do...
متن کاملCharacterization of signed paths and cycles admitting minus dominating function
If G = (V, E, σ) is a finite signed graph, a function f : V → {−1, 0, 1} is a minusdominating function (MDF) of G if f(u) +summation over all vertices v∈N(u) of σ(uv)f(v) ≥ 1 for all u ∈ V . In this paper we characterize signed paths and cycles admitting an MDF.
متن کاملGirth , minimum degree and transversals of longest paths ∗
We provide conditions on the minimum degree, the girth and the length of a longest path for a digraph to have the following property: Every longest path intersects every maximal independent set. Digraphs with this property satisfy, in a strong sense, the Laborde-PayanXuong conjecture (see [10]).
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: Journal of Graph Theory
سال: 2016
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.22021