Unsolved problems presented at the Julius Petersen Graph Theory Conference
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چکیده
منابع مشابه
Generation and properties of snarks
For many of the unsolved problems concerning cycles and matchings in graphs it is known that it is su cient to prove them for snarks, the class of nontrivial 3-regular graphs which cannot be 3-edge coloured. In the rst part of this paper we present a new algorithm for generating all non-isomorphic snarks of a given order. Our implementation of the new algorithm is 14 times faster than previous ...
متن کاملJulius Petersen's theory of regular graphs
Mulder, H.M., Julius Petersen’s theory of regular graphs, Discrete Mathematics 100 (1992) 157-17s. In 1891 the Danish mathematician Julius Petersen (1839-1910) published a paper on the factorization of regular graphs. This was the first paper in the history of mathematics to contain fundamental results explicitly in graph theory. In this report Petersen’s results are analysed and their developm...
متن کاملMatching preclusion and conditional matching preclusion problems for the folded Petersen cube
The matching preclusion number of an even graph is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of an even graph was introduced to look for obstruction sets beyond those induced by a single vertex...
متن کاملOn a Conjecture Concerning the Petersen Graph: Part II
Robertson conjectured that the only 3-connected, internally 4-connected graph of girth 5 in which every odd cycle of length greater than 5 has a chord is the Petersen graph. We provide a counterexample to this conjecture.
متن کاملOn Voltage Graphs and Cages
Using voltage graphs, we construct the the smallest known trivalent graph of girth 16. The graph has 960 vertices and is a lift of the Petersen graph. By way of preparation, other lifts of the Petersen graph are discussed. AMS Subject Classifications: 05C25, 05C35
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عنوان ژورنال:
- Discrete Mathematics
دوره 101 شماره
صفحات -
تاریخ انتشار 1992