Results 41 to 50 of about 709,702 (295)
On the Number of 1-Factors of Locally Finite Graphs [PDF]
, 1983 Every infinite locally finite graph with exactly one 1-factor is at most 2-connected is shown.
Francois Bry, Bry, François
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An introduction of F-graphs, a graph-theoretic representation of natural numbers
International Journal of Mathematics and Mathematical Sciences, 1992 A special type of family graphs (F-graphs, for brevity) are introduced. These are cactus-type graphs which form infinite families under an attachment operation. Some of the characterizing properties of F-graphs are discussed.
E. J. Farrell
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Planar and infinite hypohamiltonian and hypotraceable graphs [PDF]
, 1976 Chvátal raised the question whether or not planar hypohamiltonian graphs exist and Grünbaum conjectured the nonexistence of such graphs. We shall describe an infinite class of planar hypohamiltonian graphs and infinite classes of planar hypotraceable ...
Thomassen, Carsten, Carsten Thomassen
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Topological groups and infinite graphs [PDF]
, 1991 We show how results concerning infinite, locally finite, vertex-symmetric graphs can be related with the structure theory of topological groups, when the latter is applied to automorphism groups of the graphs. In particular, we discuss polynomial growth,
Woess, Wolfgang
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The Colouring Number of Infinite Graphs [PDF]
Combinatorica, 2019 We show that, given an infinite cardinal $μ$, a graph has colouring number at most $μ$ if and only if it contains neither of two types of subgraph. We also show that every graph with infinite colouring number has a well-ordering of its vertices that simultaneously witnesses its colouring number and its cardinality.
Nathan J. Bowler +3 more
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Note on robust coloring of planar graphs [PDF]
Opuscula MathematicaWe consider the robust chromatic number \(\chi_1(G)\) of planar graphs \(G\) and show that there exists an infinite family of planar graphs \(G\) with \(\chi_1(G) = 3\), thus solving a recent problem of Bacsó et al.
František Kardoš +2 more
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The Distinguishing Index of Infinite Graphs [PDF]
The Electronic Journal of Combinatorics, 2015 The distinguishing index $D^\prime(G)$ of a graph $G$ is the least cardinal $d$ such that $G$ has an edge colouring with $d$ colours that is only preserved by the trivial automorphism. This is similar to the notion of the distinguishing number $D(G)$ of a graph $G$, which is defined with respect to vertex colourings.We derive several bounds for ...
Broere, Izak, Pilsniak, Monika
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Infinite generalized friendship graphs [PDF]
, 1984 We give necessary and sufficient conditions for the existence of infinite generalized friendship graphs and show that there are 2° non-isomorphic ones of each admissible order c and chromatic number.
Hahn, Geňa, Delorme, Charles
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On P-transitive graphs and applications [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 We introduce a new class of graphs which we call P-transitive graphs, lying between transitive and 3-transitive graphs. First we show that the analogue of de Jongh-Sambin Theorem is false for wellfounded P-transitive graphs; then we show that the mu ...
Giacomo Lenzi
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On infinite outerplanar graphs [PDF]
, 1990 summary:In this Note, we study infinite graphs with locally finite outerplane embeddings, given a characterization by forbidden ...
Boza, L. +6 more
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