Results 21 to 30 of about 59,293 (196)
Unified bijections for maps with prescribed degrees and girth [PDF]
, 2012 This article presents unified bijective constructions for planar maps, with control on the face degrees and on the girth. Recall that the girth is the length of the smallest cycle, so that maps of girth at least $d=1,2,3$ are respectively the general ...
Bernardi, Olivier, Fusy, Eric
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American Journal of Neuroradiology, 2014 It is now official: We Americans are no longer the heaviest in the Western World. This ignominious claim belongs south of the border, to Mexico. The obesity rate of Mexicans (32.8%) has now surpassed that of Americans (31.8%).
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On Some Properties of Antipodal Partial Cubes
Discussiones Mathematicae Graph Theory, 2020 We prove that an antipodal bipartite graph is a partial cube if and only it is interval monotone. Several characterizations of the principal cycles of an antipodal partial cube are given.
Polat Norbert
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Fractional colorings of cubic graphs with large girth [PDF]
, 2010 We show that every (sub)cubic n-vertex graph with sufficiently large girth has fractional chromatic number at most 2.2978 which implies that it contains an independent set of size at least 0.4352n.
Kardos, Frantisek +2 more
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Ars Mathematica Contemporanea, 2023 Summary: Let \(\Gamma\) denote a finite, connected, simple graph. For an edge \(e\) of \(\Gamma\) let \(n(e)\) denote the number of girth cycles containing \(e\). For a vertex \(v\) of \(\Gamma\) let \(\{e_1, e_2, \dots, e_k\}\) be the set of edges incident to \(v\) ordered such that \(n(e_1) \leq n(e_2) \leq \cdots \leq n(e_k)\). Then \((n(e_1), n(e_2)
Kiss, György +2 more
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IEEE Access, 2021 Multitype quasi-cyclic (QC) low-density parity-check (LDPC) codes are a class of protograph LDPC codes lifted cyclically from protographs with multiple edges, represented by two weight and slope matrices.
Farzaneh Abedi, Mohammad Gholami
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Exhaustive generation of $k$-critical $\mathcal H$-free graphs [PDF]
, 2015 We describe an algorithm for generating all $k$-critical $\mathcal H$-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many $4$-critical $(P_7,C_k)$-free graphs, for both $k=4$ and $k=5$.
B Randerath +17 more
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, 2015 We show that the abelian girth of a graph is at least three times its girth. We prove an analogue of the Moore bound for the abelian girth of regular graphs, where the degree of the graph is fixed and the number of vertices is large. We conclude that one could try to improve the Moore bound for graphs of fixed degree and many vertices by trying to ...
Friedman, Joel +2 more
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Discrete Applied Mathematics, 2010 this paper has been withdrawn because it has been ...
Siham Bekkai, Mekkia Kouider
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Coloring, sparseness and girth [PDF]
Israel Journal of Mathematics, 2016 An $r$-augmented tree is a rooted tree plus $r$ edges added from each leaf to ancestors. For $d,g,r\in\mathbb{N}$, we construct a bipartite $r$-augmented complete $d$-ary tree having girth at least $g$. The height of such trees must grow extremely rapidly in terms of the girth. Using the resulting graphs, we construct sparse non-$k$-choosable bipartite
Alon, Noga +4 more
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