共查询到20条相似文献,搜索用时 93 毫秒
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Alexander Grigoriev Bert Marchal Natalya Usotskaya Ioan Todinca 《Discrete Applied Mathematics》2012,160(7-8):1262-1269
Given a graph with tree-width , branch-width , and side size of the largest square grid-minor , it is known that . In this paper, we introduce another approach to bound the side size of the largest square grid-minor specifically for planar graphs. The approach is based on measuring the distances between the faces in an embedding of a planar graph. We analyze the tightness of all derived bounds. In particular, we present a class of planar graphs where . 相似文献
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The -power graph of a graph is a graph with the same vertex set as , in that two vertices are adjacent if and only if, there is a path between them in of length at most . A -tree-power graph is the -power graph of a tree, a -leaf-power graph is the subgraph of some -tree-power graph induced by the leaves of the tree.We show that (1) every -tree-power graph has NLC-width at most and clique-width at most , (2) every -leaf-power graph has NLC-width at most and clique-width at most , and (3) every -power graph of a graph of tree-width has NLC-width at most , and clique-width at most . 相似文献
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Let be a 2-regular graph with vertices and assume that has a strong vertex-magic total labeling. It is shown that the four graphs , , and also have a strong vertex-magic total labeling. These theorems follow from a new use of carefully prescribed Kotzig arrays. To illustrate the power of this technique, we show how just three of these arrays, combined with known labelings for smaller 2-regular graphs, immediately provide strong vertex-magic total labelings for 68 different 2-regular graphs of order 49. 相似文献
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Yehong Shao 《Discrete Mathematics》2018,341(12):3441-3446
Let be a graph and be its line graph. In 1969, Chartrand and Stewart proved that , where and denote the edge connectivity of and respectively. We show a similar relationship holds for the essential edge connectivity of and , written and , respectively. In this note, it is proved that if is not a complete graph and does not have a vertex of degree two, then . An immediate corollary is that for such graphs , where the vertex connectivity of the line graph
and the second iterated line graph are written as and respectively. 相似文献
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Boštjan Brešar 《Discrete Mathematics》2017,340(10):2398-2401
A long-standing Vizing’s conjecture asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers; one of the most significant results related to the conjecture is the bound of Clark and Suen, , where stands for the domination number, and is the Cartesian product of graphs and . In this note, we improve this bound by employing the 2-packing number of a graph into the formula, asserting that . The resulting bound is better than that of Clark and Suen whenever is a graph with , and in the case has diameter 2 reads as . 相似文献
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Carl Johan Casselgren Hrant H. Khachatrian Petros A. Petrosyan 《Discrete Mathematics》2018,341(3):627-637
An interval-coloring of a multigraph is a proper edge coloring with colors such that the colors of the edges incident with every vertex of are colored by consecutive colors. A cyclic interval-coloring of a multigraph is a proper edge coloring with colors such that the colors of the edges incident with every vertex of are colored by consecutive colors, under the condition that color is considered as consecutive to color . Denote by () and () the minimum and maximum number of colors in a (cyclic) interval coloring of a multigraph , respectively. We present some new sharp bounds on and for multigraphs satisfying various conditions. In particular, we show that if is a -connected multigraph with an interval coloring, then . We also give several results towards the general conjecture that for any triangle-free graph with a cyclic interval coloring; we establish that approximate versions of this conjecture hold for several families of graphs, and we prove that the conjecture is true for graphs with maximum degree at most . 相似文献
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Let and be the domination number and the game domination number of a graph , respectively. In this paper -maximal graphs are introduced as the graphs for which holds. Large families of -maximal graphs are constructed among the graphs in which their sets of support vertices are minimum dominating sets. -maximal graphs are also characterized among the starlike trees, that is, trees which have exactly one vertex of degree at least . 相似文献
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Aysel Erey 《Discrete Mathematics》2018,341(5):1419-1431
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A star edge-coloring of a graph is a proper edge coloring such that every 2-colored connected subgraph of is a path of length at most 3. For a graph , let the list star chromatic index of , , be the minimum such that for any -uniform list assignment for the set of edges, has a star edge-coloring from . Dvo?ák et al. (2013) asked whether the list star chromatic index of every subcubic graph is at most 7. In Kerdjoudj et al. (2017) we proved that it is at most 8. In this paper we consider graphs with any maximum degree, we proved that if the maximum average degree of a graph is less than (resp. 3), then (resp. ). 相似文献
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Vahan V. Mkrtchyan Samvel S. Petrosyan Gagik N. Vardanyan 《Discrete Mathematics》2010,310(10-11):1588-1613
For and a cubic graph let denote the maximum number of edges that can be covered by matchings. We show that and . Moreover, it turns out that . 相似文献