Results 71 to 80 of about 119,166 (199)
Characterizations of outerplanar graphs
Discrete Mathematics, 1979 AbstractThe paper presents several characterizations of outerplanar graphs, some of them are counterparts of the well-known characterizations of planar graphs and the other provide very efficient tools for outerplanarity testing, coding (i.e. isomorphism testing), and counting such graphs.
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On the bend-number of planar and outerplanar graphs [PDF]
Discrete Applied Mathematics, 2012 appears in proceedings of 10th Latin American Symposium on Theoretical Informatics (LATIN 2012)
Heldt, Daniel +2 more
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On the Relationships between Zero Forcing Numbers and Certain Graph Coverings
Special Matrices, 2014 The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced paths in the graph that cover all ...
Taklimi Fatemeh Alinaghipour +2 more
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Random graphs embeddable in order‐dependent surfaces
Random Structures &Algorithms, Volume 64, Issue 4, Page 940-985, July 2024.Abstract Given a ‘genus function’ g=g(n)$$ g=g(n) $$, we let Eg$$ {\mathcal{E}}^g $$ be the class of all graphs G$$ G $$ such that if G$$ G $$ has order n$$ n $$ (i.e., has n$$ n $$ vertices) then it is embeddable in a surface of Euler genus at most g(n)$$ g(n) $$.
Colin McDiarmid, Sophia Saller
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An efficient g‐centroid location algorithm for cographs
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 9, Page 1405-1413, 2005., 2005 In 1998, Pandu Rangan et al. Proved that locating the g‐centroid for an arbitrary graph is 𝒩𝒫‐hard by reducing the problem of finding the maximum clique size of a graph to the g‐centroid location problem. They have also given an efficient polynomial time algorithm for locating the g‐centroid for maximal outerplanar graphs, Ptolemaic graphs, and split ...
V. Prakash
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On the colorings of outerplanar graphs
Discrete Mathematics, 1995 AbstractIn this paper, we have studied seven colorings of outerplanar graphs. Two main conclusions have been proved: if G is an outerplanar graph without cut vertex and Δ(G) ⩾ 6, then (i) χef(G) = Δ(G), and (ii) χvef(G) = Δ(G) + 1, where χef and χvef are the edge-face chromatic number and the entire chromatic number of G, respectively, and Δ(G) is the ...
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On tree decompositions whose trees are minors
Journal of Graph Theory, Volume 106, Issue 2, Page 296-306, June 2024.Abstract In 2019, Dvořák asked whether every connected graph G $G$ has a tree decomposition ( T , B ) $(T,{\rm{ {\mathcal B} }})$ so that T $T$ is a subgraph of G $G$ and the width of ( T , B ) $(T,{\rm{ {\mathcal B} }})$ is bounded by a function of the treewidth of G $G$.
Pablo Blanco +5 more
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The chromatic sum of a graph: history and recent developments
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 30, Page 1563-1573, 2004., 2004 The chromatic sum of a graph is the smallest sum of colors among all proper colorings with natural numbers. The strength of a graph is the minimum number of colors necessary to obtain its chromatic sum. A natural generalization of chromatic sum is optimum cost chromatic partition (OCCP) problem, where the costs of colors can be arbitrary positive ...
Ewa Kubicka
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A graph and its complement with specified properties I: connectivity
International Journal of Mathematics and Mathematical Sciences, 1979 We investigate the conditions under which both a graph G and its complement G¯ possess a specified property. In particular, we characterize all graphs G for which G and G¯ both (a) have connectivity one, (b) have line-connectivity one, (c) are 2 ...
Jin Akiyama, Frank Harary
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The product structure of squaregraphs
Journal of Graph Theory, Volume 105, Issue 2, Page 179-191, February 2024.Abstract A squaregraph is a plane graph in which each internal face is a 4‐cycle and each internal vertex has degree at least 4. This paper proves that every squaregraph is isomorphic to a subgraph of the semistrong product of an outerplanar graph and a path.
Robert Hickingbotham +3 more
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