As a variation on the $t$-Equal Union Property ($t$-EUP) introduced by Lindström, we introduce the $t$-Equal Valence Property ($t$-EVP) for hypergraphs: a hypergraph satisfies the $t$-EVP if there are $t$ pairwise edge-disjoint subhypergraphs such that for each vertex $v$, the degree of $v$ in all $t$ subhypergraphs is the same. In the $t$-EUP, the subhypergraphs just have the same sets of vertices with positive degree. For both the $2$-EUP and the $2$-EVP, we characterize the graphs satisfying the property and determine the maximum number of edges in a graph not satisfying it. We also study the maximum number of edges in both $k$-uniform and general hypergraphs not satisfying the $t$-EVP.
Ilkyoo Choi
1
;
Jaehoon Kim
1
;
Amelia Tebbe
1
;
Douglas B. West
2
1
University of Illinois at Urbana-Champaign
2
Zhejiang Normal University
and University of Illinois at Urbana-Champaign,
Ilkyoo Choi; Jaehoon Kim; Amelia Tebbe; Douglas B. West. Equicovering subgraphs of graphs and hypergraphs. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3999
@article{10_37236_3999,
author = {Ilkyoo Choi and Jaehoon Kim and Amelia Tebbe and Douglas B. West},
title = {Equicovering subgraphs of graphs and hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {1},
doi = {10.37236/3999},
zbl = {1300.05197},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3999/}
}
TY - JOUR
AU - Ilkyoo Choi
AU - Jaehoon Kim
AU - Amelia Tebbe
AU - Douglas B. West
TI - Equicovering subgraphs of graphs and hypergraphs
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/3999/
DO - 10.37236/3999
ID - 10_37236_3999
ER -
%0 Journal Article
%A Ilkyoo Choi
%A Jaehoon Kim
%A Amelia Tebbe
%A Douglas B. West
%T Equicovering subgraphs of graphs and hypergraphs
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/3999/
%R 10.37236/3999
%F 10_37236_3999
