A note on graphs with purely imaginary per-spectrum

by   Hitesh Wankhede, et al.
Indian Institute of Technology, Indore
Indian Institute of Science Education and Research (IISER), Pune

In 1983, Borowiecki and Jóźwiak posed an open problem of characterizing graphs with purely imaginary per-spectrum. The most general result, although a partial solution, was given in 2004 by Yan and Zhang, who show that if a graph contains no subgraph which is an even subdivision of K_2,3, then it has purely imaginary per-spectrum. Zhang and Li in 2012 proved that such graphs are planar and admit a pfaffian orientation. In this article, we describe how to construct graphs with purely imaginary per-spectrum having a subgraph which is an even subdivision of K_2,3 (planar and nonplanar) using coalescence of rooted graphs.


page 1

page 2

page 3

page 4


The Densest k Subgraph Problem in b-Outerplanar Graphs

We give an exact O(nk^2) algorithm for finding the densest k subgraph in...

Robbins and Ardila meet Berstel

In 1996, Neville Robbins proved the amazing fact that the coefficient of...

The structure of k-planar graphs

Dujmović et al. (FOCS 2019) recently proved that every planar graph is a...

A Fast Algorithm for the Product Structure of Planar Graphs

Dujmović et al (FOCS2019) recently proved that every planar graph G is a...

Resolving the Steiner Point Removal Problem in Planar Graphs via Shortcut Partitions

Recently the authors [CCLMST23] introduced the notion of shortcut partit...

Quantum isomorphism is equivalent to equality of homomorphism counts from planar graphs

Over 50 years ago, Lovász proved that two graphs are isomorphic if and o...

The Dimension Spectrum Conjecture for Planar Lines

Let L_a,b be a line in the Euclidean plane with slope a and intercept b....

Please sign up or login with your details

Forgot password? Click here to reset