Premium
Sequentially embeddable graphs
Author(s) -
Autry Jackson,
O'Neill Christopher
Publication year - 2020
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.22524
Subject(s) - combinatorics , planar graph , mathematics , embedding , book embedding , planar straight line graph , outerplanar graph , graph , discrete mathematics , planar , polyhedral graph , 1 planar graph , line graph , pathwidth , computer science , computer graphics (images) , artificial intelligence
We call a (not necessarily planar) embedding of a graph G in the plane sequential if its vertices lie in Z 2 and the line segments between adjacent vertices contain no interior integer points. In this note, we prove (a) a graph G has a sequential embedding if and only if G is 4‐colorable and (b) if G is planar, then G has a sequential planar embedding.