Geodesic
Maximum degree growth of the iterated line graph
The electronic journal of combinatorics, Tome 6 (1999)
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Let $\Delta_k$ denote the maximum degree of the $k^{\rm th}$ iterated line graph $L^k(G)$. For any connected graph $G$ that is not a path, the inequality $\Delta_{k+1}\leq 2\Delta_k-2$ holds. Niepel, Knor, and Šoltés have conjectured that there exists an integer $K$ such that, for all $k\geq K$, equality holds; that is, the maximum degree $\Delta_k$ attains the greatest possible growth. We prove this conjecture using induced subgraphs of maximum degree vertices and locally maximum vertices.
DOI : 10.37236/1460
Classification : 05C75, 05C12
Mots-clés : line graph, maximum degree 
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     author = {Stephen G. Hartke and Aparna W. Higgins},
     title = {Maximum degree growth of the iterated line graph},
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     year = {1999},
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     doi = {10.37236/1460},
     zbl = {0920.05058},
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Stephen G. Hartke; Aparna W. Higgins. Maximum degree growth of the iterated line graph. The electronic journal of combinatorics, Tome 6 (1999). doi: 10.37236/1460

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