Bibliographic Details
| Title: |
The intersection of a random geometric graph with an Erdős–Rényi graph. |
| Authors: |
Bennett, Patrick1 (AUTHOR), Frieze, Alan1,2 (AUTHOR) alan@random.math.cmu.edu, Pegden, Wesley1,2 (AUTHOR) |
| Source: |
Discrete Applied Mathematics. Jun2026, Vol. 386, p16-24. 9p. |
| Subjects: |
Random graphs, Intersection graph theory, Independent sets, Mathematical connectedness, Hamiltonian graph theory, Graph coloring |
| Abstract: |
We study the intersection of a random geometric graph with an Erdős–Rényi graph. Specifically, we generate the random geometric graph G (n , r) by choosing n points uniformly at random from D = [ 0 , 1 ] 2 and joining any two points whose Euclidean distance is at most r. We let G (n , p) be the classical Erdős–Rényi graph, i.e. it has n vertices and every pair of vertices is adjacent with probability p independently. In this note we study G (n , r , p) ≔ G (n , r) ∩ G (n , p). One way to think of this graph is that we take G (n , r) and then randomly delete edges with probability 1 − p independently. We consider the clique number, independence number, connectivity, Hamiltonicity, chromatic number, and diameter of this graph where both p (n) → 0 and r (n) → 0 ; the same model was studied by Kahle et al. (2023) for r (n) → 0 but p fixed. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
