[كتاب][B] Geodesic convexity in graphs

IM Pelayo - 2013‏ - Springer
This monograph is intended to present the current state of the art of the so-called theory of
geodesic convexity in finite, simple, connected graphs. It has been designed with the …

On the Carathéodory number for the convexity of paths of order three

RM Barbosa, EMM Coelho, MC Dourado… - SIAM Journal on Discrete …, 2012‏ - SIAM
Let G be a finite, simple, and undirected graph and let S be a set of vertices of G. If no vertex
of G that does not belong to S has two neighbors in S, then S is P_3-convex. The P_3 …

Maximize a monotone function with a generic submodularity ratio

Q Nong, T Sun, S Gong, Q Fang, D Du… - … Conference on Algorithmic …, 2019‏ - Springer
Generic submodularity ratio γ γ is a general measurement to characterize how close a
nonnegative monotone set function is to be submodular. In this paper, we make a systematic …

Geodetic Number versus Hull Number in -Convexity

CC Centeno, LD Penso, D Rautenbach… - SIAM Journal on Discrete …, 2013‏ - SIAM
We study the graphs G for which the hull number h(G) and the geodetic number g(G) with
respect to P_3-convexity coincide. These two parameters correspond to the minimum …

Bootstrap percolation in strong products of graphs

B Brešar, J Hedžet - arxiv preprint arxiv:2307.06623, 2023‏ - arxiv.org
Given a graph $ G $ and assuming that some vertices of $ G $ are infected, the $ r $-
neighbor bootstrap percolation rule makes an uninfected vertex $ v $ infected if $ v $ has at …

-Neighbor bootstrap percolation on grids

J Hedžet, MA Henning - arxiv preprint arxiv:2307.14033, 2023‏ - arxiv.org
Given a graph $ G $ and assuming that some vertices of $ G $ are infected, the $ r $-
neighbor bootstrap percolation rule makes an uninfected vertex $ v $ infected if $ v $ has at …

[HTML][HTML] Inapproximability results for graph convexity parameters

EMM Coelho, MC Dourado, RM Sampaio - Theoretical Computer Science, 2015‏ - Elsevier
In this paper, we prove several inapproximability results on the P 3-convexity and the
geodesic convexity in graphs. We prove that determining the P 3-hull number and the …

[HTML][HTML] Complexity aspects of the triangle path convexity

MC Dourado, RM Sampaio - Discrete Applied Mathematics, 2016‏ - Elsevier
In a triangle path v 1,…, vt of a graph G no edges exist joining vertices vi and vj such that| j−
i|> 2. A set S⊆ V (G) is convex in the triangle path convexity of G, or t-convex, if the vertices …

Bootstrap percolation and -hull number in direct products of graphs

B Brešar, J Hedžet, R Herrman - arxiv preprint arxiv:2403.10957, 2024‏ - arxiv.org
The $ r $-neighbor bootstrap percolation is a graph infection process based on the update
rule by which a vertex with $ r $ infected neighbors becomes infected. We say that an initial …

[HTML][HTML] Graphs with few P4's under the convexity of paths of order three

V Campos, RM Sampaio, A Silva… - Discrete Applied …, 2015‏ - Elsevier
A graph is (q, q− 4) if every subset of at most q vertices induces at most q− 4 P 4's. It
therefore generalizes some different classes, as cographs and P 4-sparse graphs. In this …