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Threecoloring trianglefree graphs on surfaces I. Extending a coloring . . .
, 2010
"... Let G be a plane graph with with exactly one triangle T and all other cycles of length at least 5, and let C be a facial cycle of G of length at most six. We prove that a 3coloring of C does not extend to a 3coloring of G if and only if C has length exactly six and there is a color x such that eit ..."
Abstract

Cited by 8 (5 self)
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Let G be a plane graph with with exactly one triangle T and all other cycles of length at least 5, and let C be a facial cycle of G of length at most six. We prove that a 3coloring of C does not extend to a 3coloring of G if and only if C has length exactly six and there is a color x such that either G has an edge joining two vertices of C colored x, or T is disjoint from C and every vertex of T is adjacent to a vertex of C colored x. This is a lemma to be used in a future paper of this series.
Foolproof
"... Mathematical proof is foolproof, it seems, only in the absence of fools I was a teenage angle trisector. In my first fulltime job, fresh out of high school, I trisected angles all day long for $1.75 an hour. My employer was a maker of voltmeters, ammeters and other electrical instruments. This was ..."
Abstract
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Mathematical proof is foolproof, it seems, only in the absence of fools I was a teenage angle trisector. In my first fulltime job, fresh out of high school, I trisected angles all day long for $1.75 an hour. My employer was a maker of voltmeters, ammeters and other electrical instruments. This was back in the analog age, when a meter had a slender pointer swinging in an arc across a scale. My job was drawing the scale. A technician would calibrate