Note on Semi-Linkage with Almost Prescribed Lengths in Large Graphs
Graphs and Combinatorics
We prove a sharp connectivity and degree sum condition for the existence of a subdivision of a multigraph in which some of the vertices are specified and the distance between each pair of vertices in the subdivision is prescribed (within one). Our proof makes use of the powerful Regularity Lemma in an easy way that highlights the extreme versatility of the lemma.
Chizmar, Emily C., Colton Magnant, Pouria Salehi Nowbandegani.
"Note on Semi-Linkage with Almost Prescribed Lengths in Large Graphs."
Graphs and Combinatorics, 32 (3): 881-886.
doi: 10.1007/s00373-015-1631-5 source: https://link.springer.com/article/10.1007%2Fs00373-015-1631-5