On Gallai's conjecture for series-parallel graphs and planar 3-trees
نویسندگان
چکیده
A path cover is a decomposition of the edges of a graph into edge-disjoint simple paths. Gallai conjectured that every connected n-vertex graph has a path cover with at most dn/2e paths. We prove Gallai’s conjecture for series-parallel graphs. For the class of planar 3-trees we show how to construct a path cover with at most b5n/8c paths, which is an improvement over the best previously known bound of b2n/3c.
منابع مشابه
Gallai's path decomposition conjecture for triangle-free planar graphs
A path decomposition of a graph G is a collection of edge-disjoint paths of G that covers the edge set of G. Gallai (1968) conjectured that every connected graph on n vertices admits a path decomposition of cardinality at most ⌊(n + 1)/2⌋. Gallai’s Conjecture has been verified for many classes of graphs. In particular, Lovász (1968) verified this conjecture for graphs with at most one vertex wi...
متن کاملToughness and spanning trees in K4mf graphs
A k-tree is a tree with maximum degree at most k, and a k-walk is a closed walk with each vertex repeated at most k times. A k-walk can be obtained from a k-tree by visiting each edge of the k-tree twice. Jackson and Wormald conjectured in 1990 that for k ≥ 2, every 1 k−1 -tough connected graph contains a spanning k-walk. This conjecture is open even for planar graphs. We confirm this conjectur...
متن کاملComplexity of Finding Non-Planar Rectilinear Drawings of Graphs
Monotone Drawings of Graphs p. 13 Upward Geometric Graph Embeddings into Point Sets p. 25 On a Tree and a Path with No Geometric Simultaneous Embedding p. 38 Difference Map Readability for Dynamic Graphs p. 50 Maximizing the Total Resolution of Graphs p. 62 Plane Drawings of Queue and Deque Graphs p. 68 An Experimental Evaluation of Multilevel Layout Methods p. 80 Orthogonal Graph Drawing with ...
متن کاملDecomposing series-parallel graphs into paths of length 3 and triangles
An old conjecture by Jünger, Reinelt and Pulleyblank states that every 2-edgeconnected planar graph can be decomposed into paths of length 3 and triangles, provided its size is divisible by 3. We prove the conjecture for a class of planar graphs including all 2-edge-connected series-parallel graphs. We also present a 2edge-connected non-planar graph that can be embedded on the torus and admits ...
متن کاملBoxicity of series-parallel graphs
The three well-known graph classes, planar graphs(P), series-parallel graphs (SP) and outer planar graphs(OP) satisfy the following proper inclusion relation: OP ⊂ SP ⊂ P . It is known that box(G) ≤ 3 if G ∈ P and box(G) ≤ 2 if G ∈ OP . Thus it is interesting to decide whether the maximum possible value of the boxicity of series-parallel graphs is 2 or 3. In this paper we construct a series-par...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1706.04130 شماره
صفحات -
تاریخ انتشار 2017