Fig 1 - uploaded by Rian Neogi
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Diagram depicting F3. Edges in the clique are not shown, and only 3 of the ui,j vertices are shown to avoid visual clutter.
Source publication
A graph is $k$-clique-extendible if there is an ordering of the vertices such that whenever two $k$-sized overlapping cliques $A$ and $B$ have $k-1$ common vertices, and these common vertices appear between the two vertices $a,b\in (A\setminus B)\cup (B\setminus A)$ in the ordering, there is an edge between $a$ and $b$, implying that $A\cup B$ is a...
Contexts in source publication
Context 1
... every pair of vertices v i and v j in K, add a vertex u i,j such that u i,j is adjacent to every vertex in K except v i and v j . Let I = {u i,j | i, j ∈ [2k − 1], i < j} be the set of all such u i,j for every pair of vertices in K. Let F k be the graph thus obtained having vertex set K ∪ I. See Figure 1 for an example that demonstrates the adjacencies between I and K when k = 3. ...
Context 2
... every pair of vertices v i and v j in K, add a vertex u i,j such that u i,j is adjacent to every vertex in K except v i and v j . Let I = {u i,j | i, j ∈ [2k − 1], i < j} be the set of all such u i,j for every pair of vertices in K. Let F k be the graph thus obtained having vertex set K ∪ I. See Figure 1 for an example that demonstrates the adjacencies between I and K when k = 3. ...
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