TY - UNPB
T1 - On the König-Egerváry Index of a Graph
AU - Jaume, Daniel A.
AU - Levit, Vadim E.
AU - Mandrescu, Eugen
AU - Molina, Gonzalo
AU - Pereyra, Kevin
PY - 2025/8/25
Y1 - 2025/8/25
N2 - A graph is said to beK\H{o}nig-Egerv\'{a}ry if its matching number equals its covering number. The difference between these two graph parameters, covering minus matching number, measures in some sense, how far a graph is from being a K\H{o}nig-Egerv\'{a}ry graph. Several properties of this difference, called the K\H{o}nig-Egerv\'{a}ry index or K\H{o}nig deficiency, are presented, including some non-trivial structural characterizations. Furthermore, it is shown that various statements involving K\H{o}nig-Egerv\'{a}ry graphs are, in fact, general statements about graphs that can be expressed in terms of their K\H{o}nig-Egerv\'{a}ry indices.
AB - A graph is said to beK\H{o}nig-Egerv\'{a}ry if its matching number equals its covering number. The difference between these two graph parameters, covering minus matching number, measures in some sense, how far a graph is from being a K\H{o}nig-Egerv\'{a}ry graph. Several properties of this difference, called the K\H{o}nig-Egerv\'{a}ry index or K\H{o}nig deficiency, are presented, including some non-trivial structural characterizations. Furthermore, it is shown that various statements involving K\H{o}nig-Egerv\'{a}ry graphs are, in fact, general statements about graphs that can be expressed in terms of their K\H{o}nig-Egerv\'{a}ry indices.
KW - maximum independent set
KW - maximum matching
KW - K\H{o}nig-Egerv\'{a}ry graph.
U2 - 10.2139/ssrn.5404413
DO - 10.2139/ssrn.5404413
M3 - Preprint
T3 - DA18610
BT - On the König-Egerváry Index of a Graph
ER -