منابع مشابه
Cycles and paths in multigraphs
We consider cycles and paths in multigraphic realizations of a degree sequence Q. in particular we show that there exists a realization of d in which no cycle has order greater than three and no path has length greater than four. In addition we show which orders of cycles and which lengths of paths exist in some realization of d.
متن کاملCycles with consecutive odd lengths
In this paper we prove that there exists an absolute constant c > 0 such that for every natural number k, every non-bipartite 2-connected graph with average degree at least ck contains k cycles with consecutive odd lengths. This implies the existence of the absolute constant d > 0 that every non-bipartite 2-connected graph with minimum degree at least dk contains cycles of all lengths modulo k,...
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A c-edge-colored multigraph has each edge colored with one of the c available colors and no two parallel edges have the same color. A proper Hamiltonian cycle is a cycle containing all the vertices of the multigraph such that no two adjacent edges have the same color. In this work we establish sufficient conditions for a multigraph to have a proper Hamiltonian cycle, depending on several parame...
متن کاملIdentifying codes of cycles with odd orders
The problem of the r -identifying code of a cycle Cn has been solved totally when n is even. Recently, S. Gravier et al. give the r -identifying code for the cycle Cn with the minimum cardinality for odd n, when n ≥ 3r + 2 and gcd(2r + 1, n) 6= 1. In this paper, we deal with the r -identifying code of the cycle Cn for odd n, when n ≥ 3r + 2 and gcd(2r + 1, n) = 1. c © 2007 Elsevier Ltd. All rig...
متن کاملGuessing Numbers of Odd Cycles
For a given number of colours, s, the guessing number of a graph is the base s logarithm of the size of the largest family of colourings of the vertex set of the graph such that the colour of each vertex can be determined from the colours of the vertices in its neighbourhood. An upper bound for the guessing number of the n-vertex cycle graph Cn is n/2. It is known that the guessing number equal...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1977
ISSN: 0095-8956
DOI: 10.1016/0095-8956(77)90058-2