A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
On Uniquely 3-Colorable Plane Graphs without Adjacent Faces of Prescribed Degrees

2019
*
Mathematics
*

A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to the permutation of the colors. For a plane graph G, two faces f 1 and f 2 of G are adjacent ( i , j )-faces if d ( f 1 ) = i, d ( f 2 ) = j, and f 1 and f 2 have a common edge, where d ( f ) is the degree of a face f. In this paper, we prove that every uniquely three-colorable plane graph has adjacent ( 3 , k )-faces, where k ≤ 5. The bound of five for k is the best possible. Furthermore, we

doi:10.3390/math7090793
fatcat:qe4glxn4qvcwhhxftq2favzm3m