2026· International Workshop on Graph-Theoretic Concepts in Computer Science· pp. 30:1-30:16· 0 citations· 39 references
Computer Science
TL;DR
Here, the most natural parameters such as the budgets d and a of the players, the vertex cover number and treewidth of the input graph, and combinations of these parameters are considered, showing that the encoding of the costs and weights of the edges has a considerable influence on the problem complexity.
The restricted edge-connectivity of a graph is the minimum size of an edge-cut whose removal leaves every component with at least two vertices. In 2024, Zhang et al. showed that the restricted edge-connectivity of any optimal $1$-planar graph belongs to $\{8,10,12\}$. In this paper, we exclude $8$ as a possible value,...
Licheng Zhang, Z. Ouyang, Yuan-Qiu Huang et al.· 0 citations
This work introduces the [Formula: see text]-Steiner-Connectivity Preservation problem where a minimum-cost set of edges are protected such that the underlying graph maintains [Formula: see text]-edge-connectivity between given terminal pairs against edge failures, assuming at most [Formula: see text] unprotected edges...
Felix Hommelsheim, Zhen-Wei Liu, Nicole Megow et al.· SIAM Journal on Discrete Mat...· 0 citations
In the three-terminal Reachability-Preserving Minimum Edge Cut problem, the input is an undirected edge-weighted graph with terminals \(s_1,s_2,t\). The objective is to delete a minimum-cost set of edges that separates \(t\) from both \(s_1\) and \(s_2\), while preserving connectivity between \(s_1\) and \(s_2\). We gi...
A matching in a graph G = (V, E) is a set M ⊆ E, such that no two edges in M share an endvertex. An edge cut in G is a set of edges C ⊆ E, such that we can partition V into two non-empty sets R and B, where C is the set of edges with one endvertex in R and one in B. A matching cut is a set of edges M ⊆ E which is both...
This paper develops an exact algorithm based on the Branch and Bound approach for solving PIDS on chordal graphs, which involves identifying the smallest group of vertices in a given network that maximizes influence throughout the network.
Y A Bekhti, M. Lalou, Méziane Aïder et al.· Pesquisa Operacional· 0 citations
It is proved that the classical cut property always produces a minimum spanning tree of a connected graph, and may be useful for large weighted networks such as communication networks, wiring connections, and transportation networks.
H. Bhapkar, Rezwan Ul Shaban, S. Mir et al.· Journal of the Nigerian Soci...· 0 citations
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