Results 31 to 40 of about 520,977 (330)
Discrete Applied Mathematics, 2019 Inspired by a famous characterization of perfect graphs due to Lov sz, we define a graph $G$ to be sum-perfect if for every induced subgraph $H$ of $G$, $ (H) + (H) \geq |V(H)|$. (Here $ $ and $ $ denote the stability number and clique number, respectively.) We give a set of $27$ graphs and we prove that a graph $G$ is sum-perfect if and only if $
Bart Litjens +2 more
openaire +2 more sources
Bounds on perfect k-domination in trees: an algorithmic approach [PDF]
Opuscula Mathematica, 2012 Let \(k\) be a positive integer and \(G = (V;E)\) be a graph. A vertex subset \(D\) of a graph \(G\) is called a perfect \(k\)-dominating set of \(G\) if every vertex \(v\) of \(G\) not in \(D\) is adjacent to exactly \(k\) vertices of \(D\). The minimum
B. Chaluvaraju, K. A. Vidya
doaj +1 more source
Perfect Outer-connected Domination in the Join and Corona of Graphs
Recoletos Multidisciplinary Research Journal, 2016 Let 𝐺 be a connected simple graph. A dominating set 𝑆 ⊆ 𝑉(𝐺) is called a perfect dominating set of 𝐺 if each 𝑢 ∈ 𝑉 𝐺 ∖ 𝑆 is dominated by exactly one element of 𝑆.
Enrico Enriquez +3 more
doaj +1 more source
Formalizing Randomized Matching Algorithms [PDF]
Logical Methods in Computer Science, 2012 Using Je\v{r}\'abek 's framework for probabilistic reasoning, we formalize the correctness of two fundamental RNC^2 algorithms for bipartite perfect matching within the theory VPV for polytime reasoning.
Dai Tri Man Le, Stephen A. Cook
doaj +1 more source
The first order convergence law fails for random perfect graphs [PDF]
, 2018 We consider first order expressible properties of random perfect graphs. That is, we pick a graph $G_n$ uniformly at random from all (labelled) perfect graphs on $n$ vertices and consider the probability that it satisfies some graph property that can be ...
Bender +10 more
core +2 more sources
NC Algorithms for Computing a Perfect Matching and a Maximum Flow in One-Crossing-Minor-Free Graphs
, 2020 In 1988, Vazirani gave an NC algorithm for computing the number of perfect matchings in $K_{3,3}$-minor-free graphs by building on Kasteleyn's scheme for planar graphs, and stated that this "opens up the possibility of obtaining an NC algorithm for ...
Eppstein, David, Vazirani, Vijay V.
core +1 more source
Hitting time results for Maker-Breaker games [PDF]
, 2010 We study Maker-Breaker games played on the edge set of a random graph. Specifically, we consider the random graph process and analyze the first time in a typical random graph process that Maker starts having a winning strategy for his final graph to ...
Alon +24 more
core +2 more sources
Perfect codes in power graphs of finite groups
Open Mathematics, 2017 The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. The enhanced power graph of a finite group is the graph whose vertex set consists of all elements of the ...
Ma Xuanlong +4 more
doaj +1 more source
OPEN PACKING NUMBER FOR SOME CLASSES OF PERFECT GRAPHS
Ural Mathematical Journal, 2020 Let \(G\) be a graph with the vertex set \(V(G)\). A subset \(S\) of \(V(G)\) is an open packing set of \(G\) if every pair of vertices in \(S\) has no common neighbor in \(G.\) The maximum cardinality of an open packing set of \(G\) is the open ...
K. Raja Chandrasekar, S. Saravanakumar
doaj +1 more source
A characterization of star-perfect graphs
AKCE International Journal of Graphs and CombinatoricsMotivated by Berge perfect graphs, we define star-perfect graphs and characterize them. For a finite simple graph G(V, E), let [Formula: see text] denote the minimum number of induced stars contained in G such that the union of their vertex sets is V(G),
G Ravindra +3 more
doaj +1 more source