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Isomorphism of two infinite-chromatic triangle-free graphs

✍ Scribed by Zsolt Tuza


Publisher
Elsevier Science
Year
1988
Tongue
English
Weight
125 KB
Volume
69
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES


Still another triangle-free infinite-chr
✍ A. GyΓ‘rfΓ‘s πŸ“‚ Article πŸ“… 1980 πŸ› Elsevier Science 🌐 English βš– 48 KB

We give a new example of a triangle-free =-chromatic graph: the vertices of G form a WX 00 matrix, V(G) = [S,j], i,. i = 1,2, . . . The vertex Ui,j is connected with every vertex of the (i + j)th column. G is triangle-free: if A has the smallest column-index among {A, B, C} c V(G) and AB, ACE E(G),

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For given n, let G be a triangle-free graph of order n with chromatic number at least 4. In this paper, we shall prove a conjecture of H/iggkvist by determining the maximal value of 6(G).

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## Abstract It is shown that the minimum number of vertices in a triangle‐free 5‐chromatic graph is at least 19.

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It follows from the results of , Gyirfis and Lehel (1985), and Kostochka (1988) that 4 ~x\* ## ~5 where x\* = max {X(G): G is a triangle-free circle graph}. We show that X\* ? 5 and thus X\* = 5. This disproves the conjecture of Karapetyan that X\* = 4 and answers negatively a question of Gyirfis

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## Abstract In this paper, it is proven that for each __k__ β‰₯ 2, __m__ β‰₯ 2, the graph Θ~__k__~(__m,…,m__), which consists of __k__ disjoint paths of length __m__ with same ends is chromatically unique, and that for each __m, n__, 2 ≀ __m__ ≀ __n__, the complete bipartite graph __K__~__m,n__~ is chr

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## Abstract The fractional chromatic number of a graph __G__ is the infimum of the total weight that can be assigned to the independent sets of __G__ in such a way that, for each vertex __v__ of __G__, the sum of the weights of the independent sets containing __v__ is at least 1. In this note we g