Construct a graph from this map where the vertices are the cities and are connected by an edge if the cities share boundaries.  Determine the least number of colors needed to re-color the map such that no two areas that share boundaries have the same color.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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  1. Construct a graph from this map where the vertices are the cities and are connected by an edge if the cities share boundaries.
  2.  Determine the least number of colors needed to re-color the map such that no two areas that share boundaries have the same color.
CALOOCAN
(NORTH)
VALENZUELA
MALABON
QUEZON CITY
CALOOCAN
MARIKINA
MANILA
SAN JUAN
MANDALUYONG-
PASIG
МАКАTI
PASAY
PATEROS
MANILA BAY
TAGUIG
PARAÑAQUE
LAGUNA
de BAY
МАР
NCR
NAVOTAS
LAS PIÑAS
MUNTINLUPA
Transcribed Image Text:CALOOCAN (NORTH) VALENZUELA MALABON QUEZON CITY CALOOCAN MARIKINA MANILA SAN JUAN MANDALUYONG- PASIG МАКАTI PASAY PATEROS MANILA BAY TAGUIG PARAÑAQUE LAGUNA de BAY МАР NCR NAVOTAS LAS PIÑAS MUNTINLUPA
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