TY - JOUR
T1 - On the Kőnig–Egerváry index of a graph
AU - Jaume, Daniel A.
AU - Levit, Vadim E.
AU - Mandrescu, Eugen
AU - Molina, Gonzalo
AU - Pereyra, Kevin
N1 - Publisher Copyright:
© 2025 Elsevier B.V.
PY - 2026/4/15
Y1 - 2026/4/15
N2 - A graph is said to be Kőnig–Egerváry if its matching number equals its vertex cover number. The difference between these two graph parameters, the vertex cover number minus the matching number, measures, in some sense, how far a graph is from being a Kőnig–Egerváry graph. Several properties of this difference, called the Kőnig–Egerváry index or Kőnig deficiency, are presented, including some nontrivial structural characterizations. Furthermore, it is shown that various statements involving Kőnig–Egerváry graphs are, in fact, general statements about graphs that can be expressed in terms of their Kőnig–Egerváry indices.
AB - A graph is said to be Kőnig–Egerváry if its matching number equals its vertex cover number. The difference between these two graph parameters, the vertex cover number minus the matching number, measures, in some sense, how far a graph is from being a Kőnig–Egerváry graph. Several properties of this difference, called the Kőnig–Egerváry index or Kőnig deficiency, are presented, including some nontrivial structural characterizations. Furthermore, it is shown that various statements involving Kőnig–Egerváry graphs are, in fact, general statements about graphs that can be expressed in terms of their Kőnig–Egerváry indices.
KW - Kőnig–Egerváry graph
KW - Maximum independent set
KW - Maximum matching
UR - https://www.scopus.com/pages/publications/105025132522
U2 - 10.1016/j.dam.2025.12.039
DO - 10.1016/j.dam.2025.12.039
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AN - SCOPUS:105025132522
SN - 0166-218X
VL - 383
SP - 139
EP - 151
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -