منابع مشابه
Simplicial Decompositions, Tree-decompositions and Graph Minors
The concepts of simplicial decompositions, tree-decompositions and simplicial tree-decompositions were all inspired by a common forerunner: the decompositions of finite graphs used by K. Wagner in his classic paper [ 13 ], in which he proved the equivalence of the 4-Colour-Conjecture to Hadwiger’s Conjecture for n = 5. To show that the 4CC implies Hadwiger’s Conjecture (for n = 5), Wagner used ...
متن کاملGraph decompositions without isolates
A. Frank (Problem session of the Fifth British Combinatorial Conference, Aberdeen, Scotland, 1975) conjectured that if G = (V, E) is a connected graph with all valencies >k and a,,..., ak > 2 are integers with C ai = / VI, then k’ may be decomposed into subsets A, ,..,, A, so that lAil = ai and the subgraph spanned by Ai in G has no isolated vertices (i= l,.... k). The case k = 2 is proved in M...
متن کاملSparsity-certifying Graph Decompositions
We describe a new algorithm, the (k, `)-pebble game with colors, and use it to obtain a characterization of the family of (k, `)-sparse graphs and algorithmic solutions to a family of problems concerning tree decompositions of graphs. Special instances of sparse graphs appear in rigidity theory and have received increased attention in recent years. In particular, our colored pebbles generalize ...
متن کاملStanton Graph Decompositions
Stanton graphs Sk (in honor of professor Ralph G. Stanton) are defined, and a new graph decomposition problem for Stanton graphs is proposed. Such decompositions of λKv for all v’s with minimum λ’s have been obtained for S3.
متن کاملGraph Ear Decompositions and Graph Embeddings
Ear decomposition of a graph has been extensively studied in relation to graph connectivity. In this paper, a connection of ear decomposition to graph embeddings is exhibited. It is shown that constructing a maximum-paired ear decomposition of a graph and constructing a maximum-genus embedding of the graph are polynomial-time equivalent. Applications of this connection are discussed.
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1992
ISSN: 0263-6115
DOI: 10.1017/s1446788700035357