geometric graph theory

endobj 41 0 obj )F,w 91 0 obj endobj endobj endobj x�%�� 44 0 obj endobj �@���S�-����@Ϛ���^���B�V{�^���N�1à��'W$y$������j��u�^K�;�����q�֌z��Mc?�� �ɠ`�����6H���W(��ͳ@no�^V8 đL9TO�S���� If,� x�+� � | <>/ExtGState<>/ProcSet[/PDF/ImageB/Text]>>/Parent 102 0 R/Annots[115 0 R 116 0 R 117 0 R 118 0 R 119 0 R]/Type/Page>> endstream �@���S�-���U�Κ���^���B�V{�^���N3|à��'W$y$v1g)�'�H�� SH u���z endobj x�%�;�0E���;�Pj��>P�,dp��k��Q�T�7 g;\�E�>��bM�C��E-%�c��Ys���q`�%�5�x|)N&xt�y�Ħ�h���*@�#�㑞����[o�{3�#%Bv�7�I��G endobj <> <> endobj 6 0 obj x�%�� endobj endstream <>stream endstream Notable geometric graphs and geometric graph theory problems include the following. When the sets are geometric objects, the result is a geometric graph. x�+� � | x�%�=�0�=��F�� ��~�8Y���%��m���B��y��C#>�V B�j*H��E]CY���@Չ!�bu k��&���y�MYR�f��G��!>'�7����f����a��8GӐpdo9�%��+���D�� �@26 endstream 56 0 obj endstream Geometric graph theory is a specialization of graph theory that studies geometric graphs. endstream Geometric graph theory is a specialization of graph theory that studies geometric graphs. <>stream <>/ExtGState<>/ProcSet[/PDF/ImageB/Text]>>/Rotate 0/Parent 102 0 R/MediaBox[0 0 612 792]/Contents[39 0 R 88 0 R 349 0 R 89 0 R 40 0 R]/Type/Page>> x�%�� 43 0 obj An intersection graph is a graph in which each vertex is associated with a set and in which vertices are connected by edges whenever the corresponding sets have a nonempty intersection. <>stream �������cTp�;n���X0N��#h%7d�p�cR�s?`5���*NC�@b⟈�ą������� ���]�d��Ђ6�_x9٢�=Vۜ�Lܔ�*��ˠLP;��\��,�=��ȏ� ���Ge������7�^ ��Z�=�`�p�s�Z1�1��ӱH��R��T��-��a% (� �$1�u�;�"��_��c�ߵ����(Ae1A���\�L�간o�. A planar straight line graph is a graph in which the vertices are embedded as points in the Euclidean plane, and the edges are embedded as non-crossing line segments. endstream (=��C|2N�=n޿�[��x)���a�:�!����rs��Wz��A�:�ͷ25 30 0 obj 138 0 obj endstream 49 0 obj endobj 135 0 obj �R\�R�������˓21 x�%�=�0�=��F���hw?P�,dp��m�6IMS��ހ�d��L$��EUAY��Z���B����7�8f|9��;4���ϐ����� endobj 83 0 obj Geometric graph theory is a specialization of graph theory that studies geometric graphs. endobj x�+� � | ��+k� =��#�GzN�?n!�z��t���a�8'�rH[)8Jq�J�ʯ;(�f~��2 It is also possible to define related flip graphs for partitions into quadrilaterals or pseudotriangles, and for higher dimensional triangulations. 70 0 obj <>stream x�+� � | endobj x�+� � | x��\ْ5��~��z�*�N�/3l&f�,1�nC'n6����W�R�Uݔ ���TeJJ���s�w6� ��ҿWߞ����|��Y�t�7ߜ}w����t����o���js��O�sf'�6�ˉ��ŷg�m��O�j�epż���~�;7F���x��0b�w�t�3����\N�1�� �)�����p�6�n��W~�.|���)]xI�};�`����.����R��H��p��b��+���=/�����ii������I¨qv��Ia|s}���k���v�O8����Q|�d�qo���b�`|{'P��z�f�G/�$�Q䡫��u\��My������g�m�Wz2a�� ���,S������[���y��˧go�{�����z���?�������G��W!� �g�0������x��]XL�S��.������ �_=��8�\n 0�+ x�%�=�0�=���J���~�8Y���%��m���B��y�;�C#>�V B�j*Ib-˺��bu5"�N��Ћ�x0�8|9L�;��y�MYQ��%��G��!>'�7����f����a��8GӐpdo9����+���D�� �g2 endobj endstream endobj <>stream endobj 75 0 obj endobj x�%ͱ 85 0 obj 24 0 obj endobj endobj x�%�� endobj endobj endobj endstream <>/ExtGState<>/ProcSet[/PDF/ImageB/Text]>>/Parent 102 0 R/Annots[291 0 R 292 0 R 293 0 R 294 0 R]/Type/Page>> () <> <>stream <>stream x�+� � | endstream When they want to tell the public what to get, they say it in curves.”—Marshall McLuhan (1911–1980), The 1-skeleton of a polyhedron or polytope is the set of vertices and edges of the polytope.  <>stream 140 0 obj <>/ExtGState<>/ProcSet[/PDF/ImageB/Text]>>/Rotate 0/Parent 102 0 R/MediaBox[0 0 612 792]/Contents[49 0 R 98 0 R 355 0 R 99 0 R 50 0 R]/Type/Page>> endobj <>stream x�+� � | endstream endstream <>stream 63 0 obj x�+� � | endstream 1 0 obj 84 0 obj endstream endobj <>stream A Levi graph of a family of points and lines has a vertex for each of these objects and an edge for every incident point-line pair. 65 0 obj 59 0 obj The flip graph of regular triangulations of a point set (projections of higher dimensional convex hulls) can also be represented as a skeleton, of the so-called. x�%�� x�%�� Geometric graph theory focuses on combinatorial and geometric properties of graphs drawn in the plane by straight-line edges (or, more generally, by edges represented by simple Jordan arcs). 53 0 obj 133 0 obj endstream 134 0 obj x�%�� 86 0 obj endobj *.Gkͨ'��q�4��^��� <>stream <>stream <>/ExtGState<>/ProcSet[/PDF/ImageB/Text]>>/Parent 102 0 R/Annots[159 0 R 160 0 R 161 0 R 162 0 R 163 0 R 164 0 R 165 0 R 166 0 R 167 0 R 168 0 R 169 0 R 170 0 R 171 0 R]/Type/Page>> endobj endstream <>stream

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