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[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 …
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
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 …
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
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 …
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 …
respect to P_3-convexity coincide. These two parameters correspond to the minimum …
Bootstrap percolation in strong products of graphs
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 rule makes an uninfected vertex $ v $ infected if $ v $ has at …
-Neighbor bootstrap percolation on grids
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 rule makes an uninfected vertex $ v $ infected if $ v $ has at …
[HTML][HTML] Inapproximability results for graph convexity parameters
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 …
geodesic convexity in graphs. We prove that determining the P 3-hull number and the …
[HTML][HTML] Complexity aspects of the triangle path convexity
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 …
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
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 …
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
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 …
therefore generalizes some different classes, as cographs and P 4-sparse graphs. In this …