نتایج جستجو برای: maximal 2 rainbow dominating function

تعداد نتایج: 3519966  

Journal: :Journal of Combinatorial Optimization 2014

Journal: :Australasian J. Combinatorics 2008
Changping Wang

A triangle-free graph is maximal if the addition of any edge produces a triangle. A set S of vertices in a graph G is called an independent dominating set if S is both an independent and a dominating set of G. The independent domination number i(G) of G is the minimum cardinality of an independent dominating set of G. In this paper, we show that i(G) ≤ δ(G) ≤ n 2 for maximal triangle-free graph...

Journal: :Appl. Math. Lett. 2012
Xingchao Deng Kai-Nan Xiang Baoyindureng Wu

For a finite simple edge-colored connected graph G (the coloring may not be proper), a rainbow path in G is a path without two edges colored the same; G is rainbow connected if for any two vertices of G, there is a rainbow path connecting them. Rainbow connection number, rc(G), of G is the minimum number of colors needed to color its edges such that G is rainbow connected. Chakraborty et al. (2...

2009
Agelos Georgakopoulos Philipp Sprüssel

We (re-)prove that in every 3-edge-coloured tournament in which no vertex is incident with all colours there is either a cyclic rainbow triangle or a vertex dominating every other vertex monochromatically.

2013
Tingting Liu Yumei Hu

A tree T , in an edge-colored graph G, is called a rainbow tree if no two edges of T are assigned the same color. A k-rainbow coloring of G is an edge coloring of G having the property that for every set S of k vertices of G, there exists a rainbow tree T in G such that S ⊆ V (T ). The minimum number of colors needed in a k-rainbow coloring of G is the k-rainbow index of G , denoted by rxk(G). ...

Journal: :Discrete Mathematics 2016
Jonathan Cutler A. J. Radcliffe

We first consider some problems related to the maximum number of dominating (or strong dominating) sets in a regular graph. Our techniques, centered around Shearer’s entropy lemma, extend to a reasonably broad class of graph parameters enumerating vertex colorings that satisfy conditions on the multiset of colors appearing in neighborhoods (either open or closed). Dominating sets and strong dom...

Roman dominating function} on a digraph $D$ with vertex set $V(D)$ is a labeling$fcolon V(D)to {0, 1, 2}$such that every vertex with label $0$ has an in-neighbor with label $2$. A set ${f_1,f_2,ldots,f_d}$ ofRoman dominating functions on $D$ with the property that $sum_{i=1}^d f_i(v)le 2$ for each $vin V(D)$,is called a {em Roman dominating family} (of functions) on $D$....

Journal: :Discrete Mathematics 2013
Timothy D. LeSaulnier Douglas B. West

Let G be an edge-colored graph with n vertices. A rainbow subgraph is a subgraph whose edges have distinct colors. The rainbow edge-chromatic number of G, written χ̂′(G), is the minimum number of rainbow matchings needed to cover E(G). An edgecolored graph is t-tolerant if it contains no monochromatic star with t+1 edges. If G is t-tolerant, then χ̂′(G) < t(t+ 1)n lnn, and examples exist with χ̂′(...

Journal: :Electr. J. Comb. 2009
Ron Aharoni Eli Berger

Given a collection of matchings M = (M1,M2, . . . ,Mq) (repetitions allowed), a matching M contained in ⋃ M is said to be s-rainbow for M if it contains representatives from s matchings Mi (where each edge is allowed to represent just one Mi). Formally, this means that there is a function φ : M → [q] such that e ∈ Mφ(e) for all e ∈ M , and |Im(φ)| > s. Let f(r, s, t) be the maximal k for which ...

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