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Arc index of spatial graphs
Author(s) -
Lee Min Jung,
No Sungjong,
Oh Seungsang
Publication year - 2019
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.22404
Subject(s) - combinatorics , mathematics , upper and lower bounds , arc (geometry) , crossing number (knot theory) , graph , index (typography) , discrete mathematics , geometry , computer science , mathematical analysis , cartography , geography , world wide web , intersection (aeronautics)
Bae and Park found an upper bound on the arc index of prime links in terms of the minimal crossing number. In this paper, we extend the definition of the arc presentation to spatial graphs and find an upper bound on the arc index α ( G ) of any spatial graph G as α ( G ) ≤ c ( G ) + e + b , where c ( G ) is the minimal crossing number of G , e is the number of edges, and b is the number of bouquet cut‐components. This upper bound is lowest possible.