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Uniquely Edge-3-Colorable Graphs and Snarks

✍ Scribed by John L. Goldwasser; Cun-Quan Zhang


Publisher
Springer Japan
Year
2000
Tongue
English
Weight
164 KB
Volume
16
Category
Article
ISSN
0911-0119

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πŸ“œ SIMILAR VOLUMES


On uniquely 3-colorable graphs
✍ Chong-Yun Chao; Zhibo Chen πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 415 KB

We show the following. (1) For each integer n> 12, there exists a uniquely 3-colorable graph with n vertices and without any triangles. (2) There exist infinitely many uniquely 3-colorable regular graphs without any triangles. It follows that there exist infinitely many uniquely k-colorable regular

On uniquely 3-colorable graphs II
✍ Chong-Yun Chao; Zhibo Chen πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 428 KB

In [2], for each non-negative integer k, we constructed a connected graph with (24)2k vertices which is uniquely 3-colorable, regular with degree k+5, and triangle-free. Here, for each positive integer n and each integer r > 5, we construct a connected graph with (26)n .2'-' vertices which is unique

Cubic graphs with three Hamiltonian cycl
✍ Andrew Thomason πŸ“‚ Article πŸ“… 1982 πŸ› John Wiley and Sons 🌐 English βš– 138 KB πŸ‘ 1 views

## Abstract The generalized Petersen graph __P__(6__k__ + 3, 2) has exactly 3 Hamiltonian cycles for __k__ β‰₯ 0, but for __k__ β‰₯ 2 is not uniquely edge colorable. This disproves a conjecture of Greenwell and Kronk [1].

Hamiltonian weights and unique 3-edge-co
✍ Cun-Quan Zhang πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 402 KB

## Abstract A (1,2)‐eulerian weight __w__ of a grph is hamiltonian if every faithful cover of __w__ is a set of two Hamilton circuits. Let __G__ be a 3‐connected cubic graph containing no subdivition of the Petersen graph. We prove that if __G__ admits a hamiltonian weight then __G__ is uniquely 3‐

Kr-Free Uniquely Vertex Colorable Graphs
✍ S. Akbari; V.S. Mirrokni; B.S. Sadjad πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 112 KB

We construct counterexamples to the conjecture of Xu (1990, J. Combin. Theory Ser. B 50, 319 320) that every uniquely r-colorable graph of order n with exactly (r&1) n&( r2 ) edges must contain a K r . ## 2001 Academic Press Harary et al. [4] constructed uniquely r-colorable graphs containing no

Maximum Ξ”-edge-colorable subgraphs of cl
✍ Vahan V. Mkrtchyan; Eckhard Steffen πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 180 KB

## Abstract A graph __G__ is class II, if its chromatic index is at least Ξ” + 1. Let __H__ be a maximum Δ‐edge‐colorable subgraph of __G__. The paper proves best possible lower bounds for |__E__(__H__)|/|__E__(__G__)|, and structural properties of maximum Δ‐edge‐colorable subgraphs. It is shown tha