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Spanning trees and spanning Eulerian subgraphs with small degrees
  • M. Hasanvand
  • Mathematics, Computer Science
  • Discret. Math.
  • 6 August 2015
Liu and Xu (1998) and Ellingham, Nam and Voss (2002) independently showed that every k -edge-connected simple graph G has a spanning tree T such that for each vertex v , d T ( v ) ? ? d ( v ) k ? + 2Expand
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Factors and Connected Factors in Tough Graphs with High Isolated Toughness
In this paper, we show that every $1$-tough graph with order and isolated toughness at least $r+1$ has a factor whose degrees are $r$, except for at most one vertex with degree $r+1$. Using thisExpand
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Packing spanning partition-connected subgraphs with small degrees
Let $G$ be a graph with $X\subseteq V(G)$ and let $l$ be an intersecting supermodular subadditive integer-valued function on subsets of $V(G)$. The graph $G$ is said to be $l$-partition-connected, ifExpand
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Modulo Orientations with Bounded Out-Degrees and Modulo Factors with Bounded Degrees
Let G be a graph, let k be a positive integer, and let p : V (G) → Zk be a mapping with |E(G)| k ≡ ∑ v∈V (G) p(v). In this paper, we show that if G is (3k − 3)-edge-connected, then G has anExpand
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The square chromatic number of the torus
The square of a graph G denoted by G 2 , is the graph with the same vertex set as G and edges linking pairs of vertices at distance at most 2 in G . Expand
C O ] 2 9 M ay 2 01 9 Bipartite partition-connected factors with small degrees
In this paper, we show that every 2m-partition-connected graph G has a bipartite m-partitionconnected factor H such that for each vertex v, dH(v) ≤ ⌈ 3 4 dG(v)⌉. A graph H is said to beExpand
Packing spanning rigid subgraphs with restricted degrees
Let $G$ be a graph and let $l$ be an integer-valued function on subsets of $V(G)$. The graph $G$ is said to be $l$-partition-connected, if for every partition $P$ of $V(G)$, $e_G(P)\ge \sum_{A\in P}Expand
Modulo $k$-Orientations and Tutte's $3$-Flow Conjecture in Graphs with Many Edge-Disjoint Spanning Trees
Let $k$ be an integer, $k\ge 3$, and let $Z_k$ be the cyclic group of order $k$. Take $\lambda_k\in [k+2, \infty)$ to be the smallest integer such that for every $\lambda_k$-edge-connected graph $G$Expand
Spanning closed walks with bounded maximum degrees of graphs on surfaces
Gao and Richter (1994) showed that every $3$-connected graph which embeds on the plane or the projective plane has a spanning closed walk meeting each vertex at most $2$ times. Brunet, Ellingham,Expand