BROWSE

Related Scientist

alexander,clifton's photo.

alexander,clifton
이산수학그룹
more info

ITEM VIEW & DOWNLOAD

Odd covers of graphs

Cited 0 time in webofscience Cited 0 time in scopus
166 Viewed 0 Downloaded
Title
Odd covers of graphs
Author(s)
Buchanan, Calum; Alexander Clifton; Culver, Eric; Nie, Jiaxi; O'Neill, Jason; Rombach, Puck; Yin, Mei
Publication Date
2023-05
Journal
JOURNAL OF GRAPH THEORY, v.104, no.2, pp.420 - 439
Publisher
WILEY
Abstract
Given a finite simple graph G $G$, an odd cover of G $G$ is a collection of complete bipartite graphs, or bicliques, in which each edge of G $G$ appears in an odd number of bicliques, and each nonedge of G $G$ appears in an even number of bicliques. We denote the minimum cardinality of an odd cover of G $G$ by b2(G) ${b}_{2}(G)$ and prove that b2(G) ${b}_{2}(G)$ is bounded below by half of the rank over F2 ${{\mathbb{F}}}_{2}$ of the adjacency matrix of G $G$. We show that this lower bound is tight in the case when G $G$ is a bipartite graph and almost tight when G $G$ is an odd cycle. However, we also present an infinite family of graphs which shows that this lower bound can be arbitrarily far away from b2(G) ${b}_{2}(G)$. Babai and Frankl proposed the "odd cover problem," which in our language is equivalent to determining b2(Kn) ${b}_{2}({K}_{n})$. In this paper, we determine that b2(Kn) ${b}_{2}({K}_{n})$ is n/2 $n\unicode{x02215}2$ when 8 divide n $8| n$ and is (n+1)/2 $(n+1)\unicode{x02215}2$ when n $n$ is equivalent to 1 or -1 $-1$ modulo 8.
URI
https://pr.ibs.re.kr/handle/8788114/13921
DOI
10.1002/jgt.22970
ISSN
0364-9024
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
Files in This Item:
There are no files associated with this item.

qrcode

  • facebook

    twitter

  • Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
해당 아이템을 이메일로 공유하기 원하시면 인증을 거치시기 바랍니다.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Browse