2015/08/30 by José F. De Jesús, De Jesús, José F., Alexander Kelmans +1
Mathematics · #05B35 #05C99 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05B35 #msc:05C99
paper · pdf · doi:10.48550/arxiv.1508.07627
arXiv admin note: text overlap with arXiv:1508.05364
arxiv created 2015/08/30 · arxiv updated 2015/09/01
In 30's Hassler Whitney considered and completely solved the problem (WP) of describing the classes of graphs G having the same cycle matroid M(G). A natural analog (WP)' of Whitney's problem (WP) is to describe the classes of graphs G having the same matroid M'(G), where M'(G) is a matroid on the edge set of G distinct from M(G). For example, the corresponding problem (WP)' = (WP)θ for the so-called bicircular matroid Mθ(G) of graph G was solved by Coulard, Del Greco and Wagner. In our previous paper [arXive:1508.05364] we introduced and studied the so-called k-circular matroids Mk(G) for every non-negative integer k that is a natural generalization of the cycle matroid M(G):= M0(G) and of the bicircular matroid Mθ(G):= M1(G) of graph G. In this paper (which is a continuation of our previous paper) we establish some properties of graphs guaranteeing that the graphs are uniquely defined by their k-circular matroids.