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Locally perfect graphs

โœ Scribed by Myriam Preissmann


Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
983 KB
Volume
50
Category
Article
ISSN
0095-8956

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Perfect and locally perfect colorings
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## Abstract We present a new algorithm for coloring perfect graphs and use it to color the parity orderable graphs, a class which strictly contains parity graphs. Also, we modify this algorithm to obtain an __O__(__m__^2^ + __n__) locally perfect coloring algorithm for parity graphs. ยฉ 1995 John Wi

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Let i be a positive integer. We generalize the chromatic number x ( G ) of G and the clique number w(G) of G as follows: The i-chromatic number of G , denoted by x Z ( G ) , is the least number k for which G has a vertex partition V,, V,, . . . , Vk: such that the clique number of the subgraph induc

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We prove the following theorem. Let G be a graph of order n and let W V(G). If |W | 3 and d G (x)+d G ( y) n for every pair of non-adjacent vertices x, y # W, then either G contains cycles C 3 ,

Locally petersen graphs
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## Abstract A graph ฮ“ is locally Petersen if, for each point __t__ of ฮ“, the graph induced by ฮ“ on all points adjacent to __t__ is isomorphic to the Petersen graph. We prove that there are exactly three isomorphism classes of connected, locally Petersen graphs and further characterize these graphs

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A coloring of a graph is locally-perfect if for every vertex u, the closed neighborhood of II contains no more than o(u) colors, where w(u) is the order of a largest clique containing u. Here is constructed, for any 4 2 3, a q + l-chromatic graph, with clique number Q, that admits a locally-perfect