TY - JOUR
T1 - Refining a chain theorem from matroids to internally 4-connected graphs
AU - Lewchalermvongs, Chanun
AU - Ding, Guoli
N1 - Publisher Copyright:
© 2024 The Author(s)
PY - 2025/2
Y1 - 2025/2
N2 - Graph theory and matroid theory are interconnected with matroids providing a way to generalize and analyze the structural and independence properties within graphs. Chain theorems, vital tools in both matroid and graph theory, enable the analysis of matroid structures associated with graphs. In a significant contribution, Chun, Mayhew, and Oxley [2] established a chain theorem for internally 4-connected binary matroids, clarifying the operations involved. Our research builds upon this by specifying the matroid result to internally 4-connected graphs. The primary goal of our research is to refine this chain theorem for matroids into a chain theorem for internally 4-connected graphs, making it more accessible to individuals less acquainted with matroid theory.
AB - Graph theory and matroid theory are interconnected with matroids providing a way to generalize and analyze the structural and independence properties within graphs. Chain theorems, vital tools in both matroid and graph theory, enable the analysis of matroid structures associated with graphs. In a significant contribution, Chun, Mayhew, and Oxley [2] established a chain theorem for internally 4-connected binary matroids, clarifying the operations involved. Our research builds upon this by specifying the matroid result to internally 4-connected graphs. The primary goal of our research is to refine this chain theorem for matroids into a chain theorem for internally 4-connected graphs, making it more accessible to individuals less acquainted with matroid theory.
KW - Chain theorem
KW - Internally 4-connected
KW - Quasi 4-connected
UR - http://www.scopus.com/inward/record.url?scp=85208185194&partnerID=8YFLogxK
U2 - 10.1016/j.aam.2024.102802
DO - 10.1016/j.aam.2024.102802
M3 - Article
AN - SCOPUS:85208185194
SN - 0196-8858
VL - 163
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
M1 - 102802
ER -