Results 11 to 20 of about 293,400 (267)
On Partition Dimension of Generalized Convex Polytopes
Journal of Mathematics, 2023 Let G be a graph having no loop or multiple edges, k−order vertex partition for G is represented by γ=γ1,γ2,…,γk. The vector rϕγ=dϕ,γ1,dϕ,γ2,dϕ,γ3⋯,dϕ,γk is the representation of vertex ϕ with respect to γ.
Syed Waqas Shah +5 more
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The partition dimension of a subdivision of a homogeneous firecracker
Electronic Journal of Graph Theory and Applications, 2020 Finding the partition dimension of a graph is one of the interesting (and uncompletely solved) problems of graph theory. For instance, the values of the partition dimensions for most kind of trees are still unknown. Although for several classes of trees
Amrullah Amrullah
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A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor [PDF]
, 2013 Motivated by the problem of testing planarity and related properties, we study the problem of designing efficient {\em partition oracles}. A {\em partition oracle} is a procedure that, given access to the incidence lists representation of a bounded ...
Levi, Reut, Ron, Dana
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A new multi-level algorithm for balanced partition problem on large scale directed graphs
Advances in Aerodynamics, 2021 Graph partition is a classical combinatorial optimization and graph theory problem, and it has a lot of applications, such as scientific computing, VLSI design and clustering etc.
Xianyue Li +4 more
doaj +1 more source
Graph homomorphisms and components of quotient graphs [PDF]
, 2016 We study how the number $c(X)$ of components of a graph $X$ can be expressed through the number and properties of the components of a quotient graph $X/\sim.$ We partially rely on classic qualifications of graph homomorphisms such as locally constrained ...
Bubboloni, Daniela
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A nonamenable "factor" of a Euclidean space [PDF]
, 2020 Answering a question of Benjamini, we present an isometry-invariant random partition of the Euclidean space $\mathbb{R}^d$, $d\geq 3$, into infinite connected indistinguishable pieces, such that the adjacency graph defined on the pieces is the 3-regular ...
Timar, Adam
core +3 more sources
Equitable partition of graphs into induced forests [PDF]
, 2015 An equitable partition of a graph $G$ is a partition of the vertex-set of $G$ such that the sizes of any two parts differ by at most one. We show that every graph with an acyclic coloring with at most $k$ colors can be equitably partitioned into $k-1 ...
Esperet, Louis +2 more
core +3 more sources
On The Partition Dimension of Disconnected Graphs
Journal of Mathematical and Fundamental Sciences, 2017 For a graph G=(V,E), a partition Ω=\{O_1,O_2,…,O_k \} of the vertex set V is called a resolving partition if every pair of vertices u,v∈V(G) have distinct representations under Ω.
Debi Oktia Haryeni +2 more
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$\mathcal{B}$-Partitions, determinant and permanent of graphs [PDF]
Transactions on Combinatorics, 2018 Let $G$ be a graph (directed or undirected) having $k$ number of blocks $B_1, B_2,\hdots,B_k$. A $\mathcal{B}$-partition of $G$ is a partition consists of $k$ vertex-disjoint subgraph $(\hat{B_1},\hat{B_1},\hdots,\hat{B_k})$ such that $\hat{B}_i$ is an ...
Ranveer Singh, Ravindra Bapat
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Partitioning a graph into highly connected subgraphs [PDF]
, 2015 Given $k\ge 1$, a $k$-proper partition of a graph $G$ is a partition ${\mathcal P}$ of $V(G)$ such that each part $P$ of ${\mathcal P}$ induces a $k$-connected subgraph of $G$. We prove that if $G$ is a graph of order $n$ such that $\delta(G)\ge \sqrt{n}$
Borozan, Valentin +6 more
core +2 more sources