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Graphs Containing Topological H
Author(s) -
Ma Jie,
Xie Qiqin,
Yu Xingxing
Publication year - 2016
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.21891
Subject(s) - combinatorics , mathematics , degree (music) , conjecture , discrete mathematics , graph , topology (electrical circuits) , physics , acoustics
Let H denote the tree with six vertices, two of which are adjacent and of degree 3. Let G be a graph andu 1 , u 2 , a 1 , a 2 , a 3 , a 4be distinct vertices of G . We characterize those G that contain a topological H in whichu 1 , u 2are of degree 3 anda 1 , a 2 , a 3 , a 4are of degree 1, which include all 5‐connected graphs. This work was motivated by the Kelmans–Seymour conjecture that 5‐connected nonplanar graphs contain topological K 5 .