2012/10/04 by Friesen, Tyler
#05C10 #57M15 #57M25 #57M27 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1210.1539
Motivated by his studies in knot theory V. Vassiliev introduced X-graphs as regular 4-valent graph with a structure of pairs of opposite edges at each vertex. He conjectured the conditions under which X-graph can be embedded into a plane respecting the the X-structure at every vertex. The conjecture was proved by V.Manturov. Here we generalize these results for graphs with vertices of valency 4 or 6, *-graphs. A problem of such generalization was posted by A.Skopenkov.