2012/11/21 by Seamone, Ben · 1 citation
#01-02 #05C15 #05C78 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.1211.5122
The 1-2-3 Conjecture, posed in 2004 by Karonski, Luczak, and Thomason, is as follows: "If G is a graph with no connected component having exactly 2 vertices, then the edges of G may be assigned weights from the set 1,2,3 so that, for any adjacent vertices u and v, the sum of weights of edges incident to u differs from the sum of weights of edges incident to v." This survey paper presents the current state of research on the 1-2-3 Conjecture and the many variants that have been proposed in its short but active history.