78 research outputs found
On Zero-free Intervals of Flow Polynomials
This article studies real roots of the flow polynomial of a
bridgeless graph . For any integer , let be the supremum in
such that has no real roots in for all
graphs with , where is the set of vertices in of
degrees larger than . We prove that can be determined by considering
a finite set of graphs and show that for ,
, and . We also prove
that for any bridgeless graph , if all roots of are
real but some of these roots are not in the set , then and has at least 9 real roots in .Comment: 26 pages, 7 figure
Counting rooted near-triangulations on the sphere
AbstractThis paper provides the results on the enumerations of rooted simple outerplanar maps, rooted outerplanar near-triangulations, rooted 2-connected near-triangulations, rooted strict 2-connected near-triangulations and rooted simple 2-connected near-triangulations. The answer to an open problem proposed by one of the authors is also provided
- …