A note on rainbow saturation number of paths
نویسندگان
چکیده
منابع مشابه
On the outer independent 2-rainbow domination number of Cartesian products of paths and cycles
Let G be a graph. A 2-rainbow dominating function (or 2-RDF) of G is a function f from V(G) to the set of all subsets of the set {1,2} such that for a vertex v ∈ V (G) with f(v) = ∅, thecondition $bigcup_{uin N_{G}(v)}f(u)={1,2}$ is fulfilled, wher NG(v) is the open neighborhoodof v. The weight of 2-RDF f of G is the value$omega (f):=sum _{vin V(G)}|f(v)|$. The 2-rainbowd...
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In a properly edge colored graph, a subgraph using every color at most once is called rainbow. In this thesis, we study rainbow cycles and paths in proper edge colorings of complete graphs, and we prove that in every proper edge coloring of Kn, there is a rainbow path on (3/4− o(1))n vertices, improving on the previously best bound of (2n + 1)/3 from [?]. Similarly, a k-rainbow path in a proper...
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LetH be a simple graph. A graph G is called anH-saturated graph ifH is not a subgraph of G, but adding any missing edge to Gwill produce a copy of H . Denote by SAT (n,H) the set of all H-saturated graphs G with order n. Then the saturation number sat(n,H) is defined as minG∈SAT (n,H) |E(G)|, and the extremal number ex(n,H) is defined as maxG∈SAT (n,H) |E(G)|. A natural question is that of whet...
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2020
ISSN: 0096-3003
DOI: 10.1016/j.amc.2020.125204