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A note on the 1-2-3 Theorem for infinite graphs by Stawiski, Marcin is a scholarly article available to read on EtoBox.

What is A note on the 1-2-3 Theorem for infinite graphs about?

Karo\'nski, {\L}uczak and Thomason conjectured in 2004 that for every finite graph without isolated edge, the edges can be assigned weights from $\{1,2,3\}$ in such a way that the endvertices of each edge have different sums of incident edge weights. This is known as the 1-2-3 Conjecture, and it was only recently proved by Keusch. We extend this result to infinite graphs in the following way. If $G$ is a graph without isolated edge, then the edges can be assigned weights from $\{1,2,3\}$ is such a way that the endvertices of each edge have different sum of incident edge weights, or these endvertices have both the same infinite degree. We also investigate the extensions of theorems about total and list versions of 1-2-3 Conjecture to infinite graphs.

Author

Stawiski, Marcin

Published

2023

Language

EN